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Search: id:A008487
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| A008487 |
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Expansion of (1-x^5 )/(1-x)^5. |
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1
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| 1, 5, 15, 35, 70, 125, 205, 315, 460, 645, 875, 1155, 1490, 1885, 2345, 2875, 3480, 4165, 4935, 5795, 6750, 7805, 8965, 10235, 11620, 13125, 14755, 16515, 18410, 20445, 22625, 24955, 27440, 30085, 32895, 35875, 39030, 42365, 45885, 49595
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Coordination sequence for 4-dimensional cyclotomic lattice Z[zeta_5].
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REFERENCES
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M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv math.CO/0508136.
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FORMULA
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a(n) is the sum of 5 consecutive tetrahedral (or pyramidal) numbers: C(n+3,3) = (n+1)(n+2)(n+3)/6 = A000292(n) for n>0, a(0) = 1. a(n) = A000292(n-4) + A000292(n-3) + A000292(n-2) + A000292(n-1) + A000292(n) for n>0, a(0) = 1. - Alexander Adamchuk (alex(AT)kolmogorov.com), May 20 2006
binomial(n+7,n+4)+binomial(n+6,n+3)+binomial(n+5,n+2)+binomial(n+4,n+1)+binomial(n+3,n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 03 2006
Equals binomial transform of [1, 4, 6, 4, 1, -1, 1, -1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 29 2008
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CROSSREFS
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Cf. A000292.
Sequence in context: A005894 A015622 A000750 this_sequence A000743 A138779 A090580
Adjacent sequences: A008484 A008485 A008486 this_sequence A008488 A008489 A008490
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KEYWORD
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nonn
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AUTHOR
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njas
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