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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

GAP

List([0..30], n-> 2*(1 +10*n^2 +5*n^4)); # G. C. Greubel, Nov 09 2019

Magma

[(n+1)^5-(n-1)^5: n in [0..30]]; // Vincenzo Librandi, Aug 27 2011

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 *)

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

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