Cody

Problem 8057. (Linear) Recurrence Equations - Generalised Fibonacci-like sequences

Solution 2016002

Submitted on 12 Nov 2019 by Tung Nguyen
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Test Suite

Test Status Code Input and Output
1   Pass
Init = [1,1]; Rules = [1,1]; N = 1:10; values_correct = [1 1 2 3 5 8 13 21 34 55]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 values = 1 1 2 3 5 8 13 21 34 55
2   Pass
Init = [2,3]; Rules = [1,1]; N = 1:10; values_correct = [2, 3, 5, 8, 13, 21, 34, 55, 89, 144]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 values = 2 3 5 8 13 21 34 55 89 144
3   Pass
Init = [1,1]; Rules = [1,1]; N = -5:5; values_correct = [5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5]; values_accepted = [nan, nan, nan, nan, nan, nan, 1, 1, 2, 3, 5]; values = recurrence_seq(N, Init, Rules); assert(isequal(values,values_correct)||isequaln(values,values_accepted))

N = 1 2 3 4 5 values = 5 -3 2 -1 1 0 1 1 2 3 5
4   Pass
Init = [1,3]; Rules = [1,1]; N = 1:10; values_correct = [1, 3, 4, 7, 11, 18, 29, 47, 76, 123]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 values = 1 3 4 7 11 18 29 47 76 123
5   Pass
Init = [1, 1, 1]; Rules = [1, 1, 0]; N = 4:21; values_correct = [2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 values = 2 2 3 4 5 7 9 12 16 21 28 37 49 65 86 114 151 200
6   Pass
Init = [0, 1]; Rules = [1, 2]; N = 4:3:19; values_correct = [5, 70, 985, 13860, 195025, 2744210]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 4 7 10 13 16 19 values = 5 70 985 13860 195025 2744210
7   Pass
Init = [3-2, 9-4]; Rules = [-6 5]; N = 1:10; values_correct = [1, 5, 19, 65, 211, 665, 2059, 6305, 19171, 58025]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 values = 1 5 19 65 211 665 2059 6305 19171 58025
8   Pass
Init = [3, 0, 2]; Rules = [1, 1, 0]; N = [28:38, 10:-1:1]; values_correct = [1983, 2627, 3480, 4610, 6107, 8090, 10717, 14197, 18807, 24914, 33004, 12, 10, 7, 5, 5, 2, 3, 2, 0, 3]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 28 29 30 31 32 33 34 35 36 37 38 10 9 8 7 6 5 4 3 2 1 values = Columns 1 through 15 1983 2627 3480 4610 6107 8090 10717 14197 18807 24914 33004 12 10 7 5 Columns 16 through 21 5 2 3 2 0 3
9   Pass
Init = [3, 0, 2]; % Perrin init Rules = [1, 1, 1]; % Tribonacci rules N = [1:15]; values_correct = [3, 0, 2, 5, 7, 14, 26, 47, 87, 160, 294, 541, 995, 1830, 3366]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 values = 3 0 2 5 7 14 26 47 87 160 294 541 995 1830 3366
10   Pass
Init = [0, 0, 1]; Rules = [1, 1, 1]; N = [1:23]; values_correct = [0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 values = Columns 1 through 15 0 0 1 1 2 4 7 13 24 44 81 149 274 504 927 Columns 16 through 23 1705 3136 5768 10609 19513 35890 66012 121415
11   Pass
Init = [0, 0, 0, 1]; Rules = [1, 1, 1, 1]; N = [20:23]; values_correct = [20569, 39648, 76424, 147312]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 20 21 22 23 values = 20569 39648 76424 147312
12   Pass
Init = [0, 0, 0, 0, 0, 0, 1]; Rules = [1, 1, 1, 1, 1, 1, 1]; N = [7:15, 19]; values_correct = [1, 1, 2, 4, 8, 16, 32, 64, 127, 2000]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 7 8 9 10 11 12 13 14 15 19 values = 1 1 2 4 8 16 32 64 127 2000
13   Pass
Init = [1, -1]; Rules = [1, -1]; N = 1:10; values_correct = [1, -1, 2, -3, 5, -8, 13, -21, 34, -55]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 values = 1 -1 2 -3 5 -8 13 -21 34 -55
14   Pass
Init = [1, -1]; Rules = [-1, 1]; N = 1:10; values_correct = [1, -1, -2, -1, 1, 2, 1, -1, -2, -1]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 values = 1 -1 -2 -1 1 2 1 -1 -2 -1
15   Pass
Init = [1, -1]; Rules = [1, 1]; N = 1:10; values_correct = [1, -1, 0, -1, -1, -2, -3, -5, -8, -13]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 values = 1 -1 0 -1 -1 -2 -3 -5 -8 -13
16   Pass
Init = [1, 1]; Rules = [2, -1]; N = 1:10; values_correct = ones(1,10); assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 values = 1 1 1 1 1 1 1 1 1 1
17   Pass
Init = [1, 2]; Rules = [2, -1]; N = 1:10; values_correct = [1, 2, 0, 4, -4, 12, -20, 44, -84, 172]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 values = 1 2 0 4 -4 12 -20 44 -84 172
18   Pass
Init = [0, 1]; Rules = [2, 1]; N = 1:10; values_correct = [0, 1, 1, 3, 5, 11, 21, 43, 85, 171]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 values = 0 1 1 3 5 11 21 43 85 171
19   Pass
Init = [1, 0, 2]; Rules = [-1 1 1]; N = 1:20; values_correct = [1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9]; assert(isequal(recurrence_seq(N, Init, Rules),values_correct))

N = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 values = 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9

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