A157748 - OEIS

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A157748

An expansion of polynomial Golay polynomial: g_4(x)=-1 + x + 2*x^4 - x^5 - x^6 - x^7 - x^9 + 2*x^10 + x^11; f(x)=1/(g_4(1/x)*x^11)=1 + 2 x - x^2 - x^4 - x^5 - x^6 + 2 x^7 + x^10 - x^11.

1, -2, 5, -12, 30, -73, 180, -444, 1095, -2699, 6653, -16399, 40421, -99632, 245580, -605324, 1492048, -3677712, 9065100, -22344336, 55075988, -135755408, 334620068, -824796535, 2033020102, -5011139791, 12351831632, -30445717146 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	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, 2, -1, 0, -1, -1, -1, 2, 0, 0, 1}}`
	REFERENCES	`J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. xxxiii.`
	FORMULA	`g_4(x)=-1 + x + 2x^4 - x^5 - x^6 - x^7 - x^9 + 2x^10 + x^11;` `f(x)=1/(g_4(1/x)*x^11)=1 + 2 x - x^2 - x^4 - x^5 - x^6 + 2 x^7 + x^10 - x^11;` `a(n)=coefficients(f(x))`
	MATHEMATICA	`f[x_] = -1 + x + 2x^4 - x^5 - x^6 - x^7 - x^9 + 2x^10 + 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: A042789 A101911 A052109 * A046170 A062423 A118649` `Adjacent sequences: A157745 A157746 A157747 * A157749 A157750 A157751`
	KEYWORD	`sign,uned`
	AUTHOR	`Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 05 2009`

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Last modified February 17 09:06 EST 2012. Contains 205999 sequences.