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A121955
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A triangle within a triangle 6 X 6 bonding graph matrix Markov: characteristic polynomial:(-4 - 2 x + x^2)(-1 + x + x^2)^2.
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0
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0, 9, 17, 72, 209, 711, 2250, 7357, 23693, 76848, 248413, 804307, 2602122, 8421705, 27251521, 88190472, 285386041, 923535567, 2988612714, 9671371877, 31297187845, 101279874144, 327748481957, 1060616489147, 3432226859754
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Simple star type boding graph. Secular roots are gloden mean/ Fibonacci-like: aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[6]] == 0, x][[n]], {n, 1, 6}] {-1.61803, -1.61803, -1.23607, 0.618034, 0.618034, 3.23607}
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FORMULA
| M = {{0, 1, 1, 1, 0, 1}, {1, 0, 1, 1, 1, 0}, {1, 1, 0, 0, 1, 1}, {1, 1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0}, {1, 0, 1, 0, 0, 0}} v[1] = {0, 1, 1, 2, 3, 5} v[n_] := v[n] = M.v[n - 1] a(n) =v[n][[1]]
Conjecture: a(n)=a(n-1)+7*a(n-2)+2*a(n-3)-4*a(n-4). G.f.: -x^2*(-9-8*x+8*x^2)/((4*x^2+2*x-1)*(x^2-x-1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 04 2009]
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MATHEMATICA
| M = {{0, 1, 1, 1, 0, 1}, {1, 0, 1, 1, 1, 0}, {1, 1, 0, 0, 1, 1}, {1, 1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0}, {1, 0, 1, 0, 0, 0}} v[1] = {0, 1, 1, 2, 3, 5} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
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CROSSREFS
| Sequence in context: A147138 A101304 A146601 * A151793 A118852 A118527
Adjacent sequences: A121952 A121953 A121954 * A121956 A121957 A121958
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 01 2006
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