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A147593 Coefficient expansion of the symmetrical polynomial: 1 - x + x^3 - 3 x^4 + x^5 - x^7 + x^8. +0
1
1, 1, 1, 0, 2, 3, 5, 3, 6, 8, 16, 16, 24, 28, 50, 61, 91, 109, 170, 220, 327, 415, 607, 800, 1164, 1536, 2192, 2928, 4172, 5616, 7921, 10705, 15049, 20460, 28638, 39027, 54453, 74451, 103662, 141996, 197288, 270704, 375632, 516096, 715258, 983661, 1362091 (list; graph; listen)
OFFSET

0,5

COMMENT

Vector Matrix Markov: M={{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {-1, 1, 0, -1, 3, -1, 0, 1}}; v[0] = Table[a[[n]], {n, 1, 8}]={1, 1, 1, 0, 2, 3, 5, 3}; v[n_] := v[n] = M.v[n - 1]; Table[v[n][[1]], {n, 0, 50}]

FORMULA

a()=Coefficient_Expansion(1 - x + x^3 - 3 x^4 + x^5 - x^7 + x^8).

MATHEMATICA

f[x_] = x^4 - x^3 - 1; g[x] = ExpandAll[ -f[x]*x^4*f[1/x]]; a = Table[SeriesCoefficient[Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]

CROSSREFS

Sequence in context: A114230 A103781 A095244 this_sequence A108396 A117367 A080184

Adjacent sequences: A147590 A147591 A147592 this_sequence A147594 A147595 A147596

KEYWORD

nonn

AUTHOR

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 08 2008

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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