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A147546
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Vertex counting using a vector matrix Markov with characteristic polynomial: 36 - 36 x + 11 x^2 - x^3.
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0
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7, 36, 186, 1002, 5622, 32466, 190806, 1132482, 6757062, 40427346, 242215926, 1452244962, 8710305702, 52252317426, 313485305046, 1880825933442, 11284697713542, 67707412226706, 406242150410166, 2437445932037922
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| This hexagon vertex substitution result is a tesselation type form that has C6 rotational symmetry.
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FORMULA
| Vertex substitutions on the pentagon: v2'=2*v2; v3'=3*v3; v6'=6*v5+12*v2; M = {{2, 0, 12}, {0, 3, 0}, {0, 0, 6}}; v(0) = {0, 6, 1}; v(n)=M.v(n-1); a(n)=Sum[v(n)[[m]],{m,1,3}].
a(n)=11*a(n-1)-36*a(n-2)+36*a(n-3) = 6*3^n-3*2^n+4*6^n. G.f.: (7-41*x+42*x^2)/((1-6x)(1-3x)(1-2x)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 09 2008]
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MATHEMATICA
| Clear[M, v, n, m, x]; M = {{2, 0, 12}, {0, 3, 0}, {0, 0, 6}}; v[0] = {0, 6, 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
| Sequence in context: A054493 A037538 A037482 * A020085 A120106 A129737
Adjacent sequences: A147543 A147544 A147545 * A147547 A147548 A147549
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 06 2008
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