A008512 Number of points on the surface of 5-dimensional cube.

2, 32, 242, 992, 2882, 6752, 13682, 24992, 42242, 67232, 102002, 148832, 210242, 288992, 388082, 510752, 660482, 840992, 1056242, 1310432, 1608002, 1953632, 2352242, 2808992, 3329282, 3918752

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (n+1)^5 - (n-1)^5.

G.f.: (2 + 22*x + 102*x^2 + 82*x^3 + 32*x^4)/(1 - 5*x + 10*x^2 - 10*x^3 + 5*x^4 - x^5). - Colin Barker, Jan 02 2012

E.g.f.: 2*(1 +15*x +45*x^2 +30*x^3 +5*x^4)*exp(x). - G. C. Greubel, Nov 09 2019

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, May 04 2021

Maple

seq((n+1)^5-(n-1)^5, n=0..30);

Mathematica

Table[10n^2*(n^2+2)+2, {n, 0, 30}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {2, 32, 242, 992, 2882}, 30] (* Harvey P. Dale, Jul 17 2014 *)

Prog

(Magma) [(n+1)^5-(n-1)^5: n in [0..30]]; // Vincenzo Librandi, Aug 27 2011
(PARI) vector(31, n, n^5-(n-2)^5) \\ G. C. Greubel, Nov 09 2019
(Sage) [2*(1 +10*n^2 +5*n^4) for n in (0..30)] # G. C. Greubel, Nov 09 2019
(GAP) List([0..30], n-> 2*(1 +10*n^2 +5*n^4)); # G. C. Greubel, Nov 09 2019

Crossrefs

Sequence in context: A053053 A053054 A224903 * A179074 A035602 A158040

Adjacent sequences: A008509 A008510 A008511 * A008513 A008514 A008515

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved