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A008516 6-dimensional centered cube numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

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

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 *)

PROG

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

(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

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

CROSSREFS

Sequence in context: A220389 A196634 A196639 * A000540 A023875 A301550

Adjacent sequences:  A008513 A008514 A008515 * A008517 A008518 A008519

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 1 05:20 EST 2021. Contains 349426 sequences. (Running on oeis4.)