A147598 - OEIS

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A147598

Coefficient expansion of the symmetrical polynomial: 1 - x - 2 x^2 + 3 x^3 + x^4 - 5 x^5 + x^6 + 3 x^7 - 2 x^8 - x^9 + x^10.

1, 1, 3, 2, 4, 3, 6, 9, 14, 23, 29, 45, 57, 88, 123, 184, 267, 382, 556, 787, 1149, 1643, 2392, 3444, 4978, 7184, 10348, 14956, 21550, 31152, 44924, 64881, 93611, 135101, 195000, 281382, 406201, 586164, 846121, 1221064, 1762399, 2543555, 3671003 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	`Vector Matrix Markov: M={{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {-1, 1, 2, -3, -1, 5, -1, -3, 2, 1}}; v[0] = Table[a[[n]], {n, 1, 10}]={1, 1, 3, 2, 4, 3, 6, 9, 14, 23}; v[n_] := v[n] = M.v[n - 1]; Table[v[n][[1]], {n, 0, 50}]`
	FORMULA	`a()=Coefficient_Expansion(1 - x - 2 x^2 + 3 x^3 + x^4 - 5 x^5 + x^6 + 3 x^7 - 2 x^8 - x^9 + x^10).` `G.f.:1/((x^5-x^4-x^3+x^2-1)*(x^5-x^3+x^2+x-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]`
	MATHEMATICA	`f[x_] = x^5 - x^4 - x^3 + x^2 - 1; g[x] = ExpandAll[ -f[x]x^5f[1/x]]; a = Table[SeriesCoefficient[Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]`
	CROSSREFS	`Sequence in context: A058708 A141731 A024856 * A023869 A024596 A175508` `Adjacent sequences: A147595 A147596 A147597 * A147599 A147600 A147601`
	KEYWORD	`nonn`
	AUTHOR	`Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 08 2008`

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Last modified February 16 06:41 EST 2012. Contains 205862 sequences.