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

1,2

Comments

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

Links

Table of n, a(n) for n=1..30.

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

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)

Example

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

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 *)

Prog

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

Crossrefs

Cf. A046092, A059986.

Sequence in context: A119286 A125342 A126500 * A200787 A250354 A146089

Adjacent sequences: A160535 A160536 A160537 * A160539 A160540 A160541

Keyword

nonn,easy

Author

Geoffrey Critzer, May 18 2009

Extensions

More terms from Harvey P. Dale, Nov 05 2017

Offset corrected by Amiram Eldar, Jan 14 2021

Status

approved