A134016 - OEIS

A134016

Inverse score permutation of an Fibonacci -anti-Fibonacci zero sum game of 2 X 2 matrices.

2, 6, 10, 23, 42, 98, 178, 415, 754, 1758, 3194, 7447, 13530, 31546, 57314, 133631, 242786, 566070, 1028458, 2397911, 4356618, 10157714, 18454930, 43028767, 78176338, 182272782, 331160282, 772119895, 1402817466, 3270752362

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OFFSET

1,1

COMMENTS

If the starting vector {0,1,1,0} means the matrix 2 X 2 MA gives A zero points and B one point, them the permutation: p = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}}; reverses that to give {1,0,0,1}. This method makes the output of matrix MA the feed for MB and the output of MB the feed of MA as: M={{MA,0},{0,MB}}

LINKS

Table of n, a(n) for n=1..30.

FORMULA

M = {{0, 1, 0, 0}, {1, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 3, 1}}; v[1] = {0, 1, 1, 0}; p = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}} v[n_] := v[n] = p.M.v[n - 1] a(n) = Sum[v[n][[i]],{i,1,4}]

Conjecture: a(n) = 4*a(n-2)+a(n-4). G.f.: x*(x^3-2*x^2-6*x-2)/(x^4+4*x^2-1). [Colin Barker, Nov 01 2012]

MATHEMATICA

M = {{0, 1, 0, 0}, {1, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 3, 1}}; v[1] = {0, 1, 1, 0}; p = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}}; v[n_] := v[n] = p.M.v[n - 1]; a = Table[Apply[Plus, v[n]], {n, 1, 50}]

CROSSREFS

Sequence in context: A342136 A049750 A295139 * A072297 A358908 A183036

Adjacent sequences: A134013 A134014 A134015 * A134017 A134018 A134019

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Jan 10 2008

STATUS

approved