A160538 a(n) = 4*(n^4-n^3).

0, 32, 216, 768, 2000, 4320, 8232, 14336, 23328, 36000, 53240, 76032, 105456, 142688, 189000, 245760, 314432, 396576, 493848, 608000, 740880, 894432, 1070696, 1271808, 1500000, 1757600, 2047032, 2370816, 2731568, 3132000

Offset: 1

Author

Geoffrey Critzer, May 18 2009

Keywords

• nonn
• easy

Comments

a(n) is the number of edges in a four-dimensional hypercube (a tesseract) having sides of length n.

Examples

			a(1) = 32 because the four dimensional unit hypercube has 32 edges.
		

Links

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

Crossrefs

Cf. A046092, A059986.

Programs

Mathematica

Table[4 (n^4 - n^3), {n, 20}]
LinearRecurrence[{5,-10,10,-5,1},{0,32,216,768,2000},30] (* Harvey P. Dale, Nov 05 2017 *)

PARI

a(n)=4*(n^4-n^3) \\ Charles R Greathouse IV, Oct 21 2022

Formula

O.g.f.: (32*x^2+56*x^3+8*x^4)/(1-x)^5.

E.g.f.: 4*exp(x)*x^2 (4 + 5 x + x^2).

From Amiram Eldar, Jan 14 2021: (Start)

Sum_{n>=2} 1/a(n) = 3/4 - Pi^2/24 - zeta(3)/4.

Sum_{n>=2} (-1)^n/a(n) = -3/4 + Pi^2/48 + log(2)/2 + 3*zeta(3)/16. (End)

Extensions

More terms from Harvey P. Dale, Nov 05 2017

Offset corrected by Amiram Eldar, Jan 14 2021