A008511 Number of points on surface of 4-dimensional cube.

0, 16, 80, 240, 544, 1040, 1776, 2800, 4160, 5904, 8080, 10736, 13920, 17680, 22064, 27120, 32896, 39440, 46800, 55024, 64160, 74256, 85360, 97520, 110784, 125200, 140816, 157680, 175840

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			G.f. = 16*x + 80*x^2 + 240*x^3 + 544*x^4 + 1040*x^5 + 1776*x^6 + 2800*x^7 + ... - _Michael Somos_, Jun 24 2018
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000583, A005917, A006003.

Programs

GAP

List([0..30], n-> 8*n*(1+n^2)); # G. C. Greubel, Nov 09 2019

Magma

[(n+1)^4-(n-1)^4: n in [0..30]]; // Vincenzo Librandi, Aug 27 2011

Maple

seq(8*n*(1+n^2), n=0..30); # G. C. Greubel, Nov 09 2019

Mathematica

Last[#]-First[#]&/@Partition[Range[-1,30]^4,3,1] (* or *) LinearRecurrence[ {4,-6,4,-1},{0,16,80,240},30] (* Harvey P. Dale, Oct 15 2012 *)

PARI

vector(31, n, 8*(n-1)*(1+(n-1)^2)) \\ G. C. Greubel, Nov 09 2019

Sage

[8*n*(1+n^2) for n in (0..30)] # G. C. Greubel, Nov 09 2019

Formula

a(n) = (n+1)^4 - (n-1)^4 = 8*n + 8*n^3.

G.f.: 16*x*(1+x+x^2)/(1-4*x+6*x^2-4*x^3+x^4). - Colin Barker, Jan 02 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), a(0)=0, a(1)=16, a(2)=80, a(3)=240. - Harvey P. Dale, Oct 15 2012

a(n) = 16 * A006003(n). - J. M. Bergot, Jul 22 2013

For n > 0, a(n) = A005917(n) + A005917(n+1) = A000583(n+1) - A000583(n-1). - Bruce J. Nicholson, Jun 19 2018

a(n) = -a(-n) for all n in Z. - Michael Somos, Jun 24 2018

E.g.f.: 8*x*(2 +3*x +x^2)*exp(x). - G. C. Greubel, Nov 09 2019