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A008515 5-dimensional centered cube numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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
LINKS
Tito Piezas, About a Ramanujan-Sata formula of level 10, a recurrence, and zeta(5)?, Mathoverflow question asked Mar 27 2017.
FORMULA
a(n) = n^5 + (n+1)^5 = 2*n^5 +5*n^4 +10*n^3 +10*n^2 +5*n +1.
From Bruno Berselli, Aug 25 2011: (Start)
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
MAPLE
seq(n^5+(n+1)^5, n=0..40);
MATHEMATICA
Sum[(Range[40]+j-2)^5, {j, 2}] (* G. C. Greubel, Nov 09 2019 *)
PROG
(PARI) a(n) = n^5+(n+1)^5;
(Magma) [n^5+(n+1)^5: n in [0..40]]; // Bruno Berselli, Aug 25 2011
(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
CROSSREFS
Apart from the first term, a subsequence of A088703.
Sequence in context: A119782 A252978 A268264 * A179995 A000539 A023874
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 18 21:02 EDT 2024. Contains 370951 sequences. (Running on oeis4.)