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A119515
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Pattern Matrix of alternating sign 5 X 5 Matrix Markov with low ratio and characteristic polynomial: x^5+5*x^4+20*x^3+20*x^2+5*x+1.
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0
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0, -1, 8, -28, 71, -150, 281, -483, 778, -1191, 1750, -2486, 3433, -4628, 6111, -7925, 10116, -12733, 15828, -19456, 23675, -28546, 34133, -40503, 47726, -55875, 65026, -75258, 86653, -99296
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..29.
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FORMULA
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G.f.:x*(x^3+2*x^2+3*x-1)/(x+1)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
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EXAMPLE
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Diagonals alternate in sign:
{{-1, 1, -1, 1, -1},
{0, -1, 1, -1, 1},
{0, 0, -1, 1, -1},
{0, 0, 0, -1,1},
{0, 0, 0, 0, -1}}
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MATHEMATICA
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M = Table[If[n > m, 0, -(-1)^(n + m), If[n < m, (-1)^(n + m), 0]], {n, 1, 5}, {m, 1, 5}]; w[1] = {0, 1, 1, 2, 3}; w[n_] := w[n] = M.w[n - 1] a = Table[w[n][[1]], {n, 1, 30}]
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CROSSREFS
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Sequence in context: A100182 A321237 A328535 * A304343 A153976 A105636
Adjacent sequences: A119512 A119513 A119514 * A119516 A119517 A119518
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula), Jul 27 2006
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STATUS
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approved
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