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A147535
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A counting vertex substitution vector matrix Markov 3x3 with characteristic polynomial:24 - 26 x + 9 x^2 - x^3
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0
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5, 18, 64, 228, 820, 2988, 11044, 41388, 157060, 602508, 2332324, 9095148, 35676100, 140586828, 555986404, 2204846508, 8762055940, 34876167948, 138988373284, 554404335468, 2212969344580
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OFFSET
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0,1
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COMMENTS
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This type of vertex cartoon substitution can be counted by this Markov method. The 3by3 model is mirror symmetric in one plane.
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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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]
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MATHEMATICA
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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}]
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CROSSREFS
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Sequence in context: A029869 A033453 A222373 * A184309 A051944 A153373
Adjacent sequences: A147532 A147533 A147534 * A147536 A147537 A147538
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula, Nov 06 2008
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STATUS
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approved
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