A143479 - OEIS

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A143479

Coefficient expansion of the McMullen transformed characteristic polynomial of the E_11 Cartan Matix: p(x)]=-2 - 167 x + 1694 x^2 - 6069 x^3 + 11210 x^4 - 12297 x^5 + 8554 x^6 -3875 x^7 + 1140 x^8 - 210 x^9 + 22 x^10 - x^11.

-1, -22, -263, -2284, -16225, -100490, -564096, -2943434, -14525316, -68623698, -313160381, -1389603972, -6026265844, -25641735564, -107383041717, -443700335414, -1812509085585, -7331932395596, -29409752732192, -117108140185676, -463355891177610, -1823137506023896 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	COMMENTS	`The polynomial is symmetric:` `h[x]=x^22h[1/x].` `It would be fairly easy to map the McMullem 22nd degree` `Salem which is related to K3 dynamics (and a tetrahedral surface) to this 22nd degree polynomial. The McMullen Salem polynomial has the ratio of` `1.3728862806447408 which is near 1/(100Alpha) the fine structure constyant.`
	FORMULA	`p(x)]=-2 - 167 x + 1694 x^2 - 6069 x^3 + 11210 x^4 - 12297 x^5 + 8554 x^6 -3875 x^7 + 1140 x^8 - 210 x^9 + 22 x^10 - x^11; q(x)=x^11*p(x+1/x); a(n)=Coefficient_Expansion(q(x)).`
	MATHEMATICA	m11 = {{2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -1, 2, -1, 0, 0, 0, 0, 0, 0, -1}, {0, 0, -1, 2, -1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0}, {0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2}}; f[x_] = CharacteristicPolynomial[m11, x]; h[x_] = ExpandAll[x^11f[x + 1/x]]; g[x] = ExpandAll[x^22h[1/x]]; a = Table[SeriesCoefficient[Series[1/g[x], {x, 0, 30}], n], {n, 0, 30}]
	CROSSREFS	`Sequence in context: A162679 A010974 A022587 * A004412 A172242 A055756` `Adjacent sequences: A143476 A143477 A143478 * A143480 A143481 A143482`
	KEYWORD	`uned,sign`
	AUTHOR	`Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 24 2008`

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Last modified February 16 04:47 EST 2012. Contains 205860 sequences.