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A147535 A counting vertex substitution vector matrix Markov 3x3 with characteristic polynomial:24 - 26 x + 9 x^2 - x^3 0
5, 18, 64, 228, 820, 2988, 11044, 41388, 157060, 602508, 2332324, 9095148, 35676100, 140586828, 555986404, 2204846508, 8762055940, 34876167948, 138988373284, 554404335468, 2212969344580 (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 3by3 model is mirror symmetric in one plane.

LINKS

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

FORMULA

Vertex substitutions are: v2'=2*v2; v3'=3*v3; v4'=4*v4=2*v2: giving the matrix: M = {{2, 0, 2}, {0, 3, 0}, {0, 0, 4}}; The five vertex start has count vector: v(0)={0,4,1}; v(n)=M.v(n-1); a(n)=Sum[v(n)[[m]],{m,1,3}].

a(n) = 9*a(n-1)-26*a(n-2)+24*a(n-3) = 2*4^n+4*3^n-2^n. G.f.: (5-27x+32x^2)/((1-2x)(1-3x)(1-4x)). [From R. J. Mathar, Nov 09 2008]

MATHEMATICA

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

CROSSREFS

Sequence in context: A284840 A301749 A222373 * A184309 A051944 A153373

Adjacent sequences:  A147532 A147533 A147534 * A147536 A147537 A147538

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Nov 06 2008

STATUS

approved

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Last modified September 16 12:41 EDT 2019. Contains 327113 sequences. (Running on oeis4.)