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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

Magma

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

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