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Search: id:A158762
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| A158762 |
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Sub-Padovan vector matrix Markov sequence:t=3;M={{0, t, 0}, {0, 0, t}, {t, 1/t^3, 0}}; |
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1
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| 1, 9, 81, 738, 6642, 59787, 544644, 4901805, 44129367, 401947281, 3617545212, 32572255824, 296637113061, 2669762715372, 24041811608757, 218918218136841, 1970298831114945, 17745398880920694, 161561679852872034
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OFFSET
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0,2
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COMMENT
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Characteristic Polynomial is:t=3;
t^3 + x/t^2 - x^3
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FORMULA
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t=3;M={{0, t, 0},
{0, 0, t},
{t, 1/t^3, 0}};
v(n)=M.v(n-1);
a(n)=v(n)[[1]]^t^n
Conjecture: a(n)=a(n-2)+729*a(n-3). G.f: -(1+9*x+80*x^2)/(-1+x^2+729*x^3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 26 2009]
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MATHEMATICA
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Clear[M, v, t, n];
M = {{0, t, 0}, {0, 0, t}, {t, 1/t^3, 0}};
v[0] = {1, 1, 1};
v[n_] := v[n] = M.v[n - 1];
CharacteristicPolynomial[M, x];
t = 3;
a = Table[t^n*v[n][[1]], {n, 0, 30}]
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CROSSREFS
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Sequence in context: A047901 A061587 A033145 this_sequence A101601 A144821 A137062
Adjacent sequences: A158759 A158760 A158761 this_sequence A158763 A158764 A158765
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 25 2009
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