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A008515 5-dimensional centered cube numbers. 2
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, 84570817, 97957299, 112988051, 129810133, 148579125 (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

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Tito Piezas, About a Ramanjuan-Sata formula of level 10, a recurrence, and zeta(5)?, Mathoverflow question asked Mar 27 2017.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

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) = +6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).  (End)

MAPLE

n^5+(n+1)^5;

PROG

(PARI) a(n) = n^5+(n+1)^5;

(MAGMA) [n^5+(n+1)^5: n in [0..37]];  // Bruno Berselli, Aug 25 2011

CROSSREFS

Apart from the first term, a subsequence of A088703.

Sequence in context: A119782 A252978 A268264 * A179995 A000539 A023874

Adjacent sequences:  A008512 A008513 A008514 * A008516 A008517 A008518

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 19 13:00 EDT 2017. Contains 290807 sequences.