OFFSET
1,2
COMMENTS
a(n) is the number of edges in a four-dimensional hypercube (a tesseract) having sides of length n.
LINKS
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
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