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A147536 A counting vertex substitution vector matrix Markov 2x2 with characteristic polynomial:12 - 7 x + x=^2 0
5, 16, 52, 172, 580, 1996, 7012, 25132, 91780, 340876, 1284772, 4902892, 18902980, 73486156, 287567332, 1131137452, 4467154180, 17696429836, 70269158692, 279526952812, 1113458765380 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This type of vertex cartoon substitution can be counted by this Markov method. The 2by2 model is has a C4 axis of rotation.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

Vertex substitutions are: v3'=3*v3; v4'=4*v4 giving the matrix: M = {{3, 0}, {0, 4}} The five vertex start has count vector: v(0)={4,1}; v(n)=M.v(n-1); a(n)=Sum[v(n)[[m]],{m,1,2}].

a(n)=7*a(n-1)-12*a(n-2) = 4*3^n+4^n. G.f.: (5-19x)/((1-4x)(1-3x)). [From R. J. Mathar, Nov 09 2008]

MATHEMATICA

Clear[M, v, n, m, x]; M = {{3, 0}, {0, 4}}; v[0] = { 4, 1}; v[n_] := v[n] = M.v[n - 1]; Table[Sum[v[n][[m]], {m, 1, 2}], {n, 0, 20}]

CROSSREFS

Sequence in context: A077840 A007343 A274492 * A173871 A108300 A041469

Adjacent sequences:  A147533 A147534 A147535 * A147537 A147538 A147539

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Nov 06 2008

STATUS

approved

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Last modified April 20 03:03 EDT 2019. Contains 322294 sequences. (Running on oeis4.)