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A008515
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5-dimensional centered cube numbers.
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3
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1, 33, 275, 1267, 4149, 10901, 24583, 49575, 91817, 159049, 261051, 409883, 620125, 909117, 1297199, 1807951, 2468433, 3309425, 4365667, 5676099, 7284101, 9237733, 11589975, 14398967, 17728249, 21647001, 26230283, 31559275, 37721517, 44811149, 52929151, 62183583, 72689825
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OFFSET
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0,2
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COMMENTS
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These are never prime, as a(n) = (2n+1)*(n^4+2*n^3+4*n^2+3*n+1). - Jonathan Vos Post, Aug 18 2011
zeta(5) = 1 / (a(1) - 1^10 / (a(2) - 2^10 / (a(3) - 3^10 / ... ))) [From Tito Piezas III mathoverflow question 265688 comment]. - Michael Somos, Jul 06 2017
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LINKS
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FORMULA
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a(n) = n^5 + (n+1)^5 = 2*n^5 +5*n^4 +10*n^3 +10*n^2 +5*n +1.
G.f.: (1+x)*(1 +26*x +66*x^2 +26*x^3 +x^4)/(1-x)^6.
a(n) = -a(-n-1).
a(n) = 6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6). (End)
E.g.f.: (1 +32*x +105*x^2 +90*x^3 +25*x^4 +2*x^5)*exp(x). - G. C. Greubel, Nov 09 2019
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MAPLE
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seq(n^5+(n+1)^5, n=0..40);
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MATHEMATICA
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PROG
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(PARI) a(n) = n^5+(n+1)^5;
(Sage) [n^5+(n+1)^5 for n in (0..40)] # G. C. Greubel, Nov 09 2019
(GAP) List([0..40], n-> n^5+(n+1)^5); # G. C. Greubel, Nov 09 2019
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CROSSREFS
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Apart from the first term, a subsequence of A088703.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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