A157746 - OEIS

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A157746

An expansion of polynomial Golay polynomial: g_2(x)=1 + x + x^5 + x^6 + x^7 + x^9 + x^11; f(x)=1/(g_2(1/x)*x^11)=1 + x^2 + x^4 + x^5 + x^6 + x^10 + x^11.

1, 0, -1, 0, 0, -1, 0, 2, 1, -1, -1, -1, -1, 0, 2, 4, 2, -4, -6, -2, 0, 2, 10, 11, -4, -17, -14, -4, 7, 22, 30, 11, -31, -57, -35, 15, 56, 80, 64, -32, -152, -160, -28, 136, 240, 228, 29, -312, -521, -324, 208 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,8`
	COMMENTS	`Characteristic matrix of of the toral inverse polynomial is:` `{{0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},` `{0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0},` `{0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},` `{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},` `{0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0},` `{0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0},` `{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},` `{0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0},` `{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0},` `{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},` `{-1, 0, -1, 0, -1, -1, -1, 0, 0, 0, -1}}`
	REFERENCES	`J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. xxxiii.`
	FORMULA	`g_2(x)=1 + x + x^5 + x^6 + x^7 + x^9 + x^11;` `f(x)=1/(g_2(1/x)*x^11)=1 + x^2 + x^4 + x^5 + x^6 + x^10 + x^11;` `a(n)=coefficients(f(x))`
	MATHEMATICA	`f[x_] = 1 + x + x^5 + x^6 + x^7 + x^9 + x^11;` `g[x] = ExpandAll[x^11*f[1/x]];` `a = Table[SeriesCoefficient[ Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]`
	CROSSREFS	`Sequence in context: A178666 A206706 A000164 * A037820 A076493 A037910` `Adjacent sequences: A157743 A157744 A157745 * A157747 A157748 A157749`
	KEYWORD	`sign,uned`
	AUTHOR	`Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 05 2009`

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Last modified February 17 09:41 EST 2012. Contains 206009 sequences.