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A008511 Number of points on surface of 4-dimensional cube. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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

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

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

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Last modified October 17 18:19 EDT 2018. Contains 316292 sequences. (Running on oeis4.)