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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 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 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)