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A036086

Centered cube numbers: a(n) = (n+1)^8+n^8.

1, 257, 6817, 72097, 456161, 2070241, 7444417, 22542017, 59823937, 143046721, 314358881, 644340577, 1245712417, 2291519777, 4038679681, 6857857921, 11270724737, 17995718017, 28003523617, 42583563041

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OFFSET

0,2

LINKS

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

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

FORMULA

G.f.: -(x^6+246*x^5+4047*x^4+11572*x^3+4047*x^2+246*x+1)*(1+x)^2 / (x-1)^9. - R. J. Mathar, Oct 13 2011

MAPLE

A036086:=n->(n+1)^8+n^8: seq(A036086(n), n=0..30); # Wesley Ivan Hurt, Feb 03 2017

MATHEMATICA

Total/@Partition[Range[0, 20]^8, 2, 1] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 257, 6817, 72097, 456161, 2070241, 7444417, 22542017, 59823937}, 30] (* Harvey P. Dale, Dec 11 2014 *)

PROG

(Magma) [(n+1)^8+n^8: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

CROSSREFS

Sequence in context: A017679 A013956 A294303 * A000542 A023877 A301552

Adjacent sequences: A036083 A036084 A036085 * A036087 A036088 A036089

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved