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A078473
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Expansion of zeta function of icosian ring.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| 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))
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LINKS
| M. Baake and R. V. Moody, Similarity submodules and root systems in four dimensions, Canad. J. Math. 51 (1999), 1258-1276.
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PROG
| (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]*d*A[n/d]))} /* Michael Somos Jun 06 2005 */
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CROSSREFS
| Cf. A035282 (nonzero terms of the sequence), A031363 (n for which a(n) is not zero), A078471..
Sequence in context: A051716 A102060 A102058 * A110800 A021645 A031364
Adjacent sequences: A078470 A078471 A078472 * A078474 A078475 A078476
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KEYWORD
| nonn,mult
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 31 2002
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