0,2

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. It doesn't appear that such marriage systems based on permutations are effective in preventing harmful combinations of genes, but they do change population growth statisics.

Kemeny,Snell and Thompson,Introduction to Finite Mathematics,1966,Printice-Hall, N,J.,Section 6, Chapter VII

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] = {{1, 0, 1}, {2, 2, 0}, {0, 2, 2}}; v[n_] := v[n] = M[n - 1].v[n - 1] a(n) =v[n][[1]]

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] = {{1, 0, 1}, {2, 2, 0}, {0, 2, 2}}; v[n_] := v[n] = M[n - 1].v[n - 1] a0 = Table[v[n][[1]], {n, 0, 25}]

Sequence in context: A032413 A066238 A101074 this_sequence A048001 A109299 A073257

Adjacent sequences: A115106 A115107 A115108 this_sequence A115110 A115111 A115112

nonn,uned

Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 03 2006