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

0,2

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).

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

Example

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

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 *)

Prog

(Magma) [(n+1)^4-(n-1)^4: n in [0..30]]; // Vincenzo Librandi, Aug 27 2011
(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
(GAP) List([0..30], n-> 8*n*(1+n^2)); # G. C. Greubel, Nov 09 2019

Crossrefs

Cf. A000583, A005917, A006003.

Sequence in context: A044584 A111732 A271992 * A130810 A212090 A212240

Adjacent sequences: A008508 A008509 A008510 * A008512 A008513 A008514

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved