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Search: id:A115108
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| A115108 |
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Marriage system row permutation vector Matrix Markov M2 intial condition. |
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+0
1
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| 1, 4, 16, 56, 156, 248, 1584, 2248, 18512, 51856, 189440, 609664, 2023808, 6579712, 21441536, 69575680, 225665024, 731127808, 2367905792, 7666302976, 24816189440, 80321511424, 259955621888, 841292972032, 2722599796736
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Using only M0 and intitial condition v[0]={1,0,1} the system is Fibonacci. The system in intial matrix sensative. The permutation of row condition is such that if the population number divides by three a permutation is selected. The Matrices are based on {aa,2ab,bb} dominant/recessive gene pairings relating father to mother.
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REFERENCES
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Kemeny,Snell and Thompson,Introduction to Finite Mathematics,1966,Printice-Hall, N,J.,Section 6, Chapter VII
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FORMULA
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M0 = {{2, 2, 0}, {1, 0, 1}, {0, 2, 2}}; M1 = {{1, 0, 1}, {2, 2, 0}, {0, 2, 2}}; M2 = {{2, 2, 0}, {0, 2, 2}, {1, 0, 1}}; M[n_] := M[n] = If[Mod[v[n][[1]], 3] == 0, M1, If[Mod[v[n][[2]], 3] == 0, M0, M2]] v[0] = {1, 1, 1}; M[0] = {{2, 2, 0}, {0, 2, 2}, {1, 0, 1}}; v[n_] := v[n] = M[n - 1].v[n - 1] a(n) =v[n][[1]]
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MATHEMATICA
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M0 = {{2, 2, 0}, {1, 0, 1}, {0, 2, 2}}; M1 = {{1, 0, 1}, {2, 2, 0}, {0, 2, 2}}; M2 = {{2, 2, 0}, {0, 2, 2}, {1, 0, 1}}; M[n_] := M[n] = If[Mod[v[n][[1]], 3] == 0, M1, If[Mod[v[n][[2]], 3] == 0, M0, M2]] v[0] = {1, 1, 1}; M[0] = {{2, 2, 0}, {0, 2, 2}, {1, 0, 1}}; v[n_] := v[n] = M[n - 1].v[n - 1] a0 = Table[v[n][[1]], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A121159 A134968 A127634 this_sequence A127393 A073388 A109634
Adjacent sequences: A115105 A115106 A115107 this_sequence A115109 A115110 A115111
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 03 2006
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