A008516 6-dimensional centered cube numbers.

1, 65, 793, 4825, 19721, 62281, 164305, 379793, 793585, 1531441, 2771561, 4757545, 7812793, 12356345, 18920161, 28167841, 40914785, 58149793, 81058105, 111045881, 149766121, 199146025, 261415793, 339138865, 435243601, 553056401, 696336265, 869310793, 1076713625, 1323823321

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

These are never prime, as a(n) = (2*n^2 + 2*n + 1) * (n^4 + 2*n^3 + 5*n^2 + 4*n + 1). - Jonathan Vos Post, Aug 17 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Programs

GAP

List([0..35], n-> n^6+(n+1)^6); # G. C. Greubel, Nov 09 2019

Magma

[(n+1)^6+n^6: n in [0..35]]; // Vincenzo Librandi, Aug 27 2011

Maple

seq(n^6+(n+1)^6, n=0..35);

Mathematica

Table[n^6 + (n+1)^6, {n,0,35}] (* Alonso del Arte, Aug 17 2011 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,65,793,4825,19721,62281,164305},30] (* Harvey P. Dale, Jun 19 2021 *)

PARI

vector(36, n, n^6+(n-1)^6) \\ G. C. Greubel, Nov 09 2019

Sage

[n^6+(n+1)^6 for n in (0..35)] # G. C. Greubel, Nov 09 2019

Formula

From Colin Barker, Jul 09 2012: (Start)

G.f.: (1 + 58*x + 359*x^2 + 604*x^3 + 359*x^4 + 58*x^5 + x^6)/(1-x)^7.

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

E.g.f.: (1 +64*x +332*x^2 +440*x^3 +205*x^4 +36*x^5 +2*x^6)*exp(x). - G. C. Greubel, Nov 09 2019