id:A078473 - OEIS Search Results

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Expansion of zeta function of icosian ring.

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1, 0, 0, 5, 6, 0, 0, 0, 10, 0, 24, 0, 0, 0, 0, 21, 0, 0, 40, 30, 0, 0, 0, 0, 31, 0, 0, 0, 60, 0, 64, 0, 0, 0, 0, 50, 0, 0, 0, 0, 84, 0, 0, 120, 60, 0, 0, 0, 50, 0, 0, 0, 0, 0, 144, 0, 0, 0, 120, 0, 124, 0, 0, 85, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 200, 0, 0, 160, 126, 91, 0, 0, 0, 0, 0, 0, 0 (list; graph; listen)

	OFFSET	`1,4`
	COMMENT	`Let zetaI(s) be the zeta function of icosian ring: zetaI(s)=zetaQ(tau)(2s)*zetaQ(tau)(2s-1) where zetaQ(tau)(s) is defined in A035187. Then zetaI(s) = sum(n>=1,a(n)/n^(2s))`
	LINKS	`M. Baake and R. V. Moody, Similarity submodules and root systems in four dimensions, Canad. J. Math. 51 (1999), 1258-1276.`
	PROGRAM	`(PARI) {a(n)=local(A); if(n<1, 0, A=direuler(p=2, n, 1/(1-X)/(1-kronecker(5, p)X)); sumdiv(n, d, A[d]dA[n/d]))} / Michael Somos Jun 06 2005 */`
	CROSSREFS	`Cf. A035282 (nonzero terms of the sequence), A031363 (n for which a(n) is not zero), A078471..` `Sequence in context: A051716 A102060 A102058 this_sequence A110800 A021645 A031364` `Adjacent sequences: A078470 A078471 A078472 this_sequence A078474 A078475 A078476`
	KEYWORD	`nonn,mult`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 31 2002`

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Last modified November 23 17:09 EST 2009. Contains 167438 sequences.

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