OFFSET
4,1
COMMENTS
Number of n permutations (n>=4) of 3 objects u,v,z, with repetition allowed, containing n-4 u's. Example: if n=4 then n-4 =(0) zero u, a(1)=16 because we have vvvv zzzz vvvz zzzv vvzv zzvz vzvv zvzz zvvv vzzz vvzz zzvv vzvz zvzv zvvz vzzv. - Zerinvary Lajos, Aug 05 2008
a(n) is the number of 3-dimensional elements in an n-cross polytope where n>=4. - Patrick J. McNab, Jul 06 2015
LINKS
H. J. Brothers, Pascal's Prism: Supplementary Material
Milan Janjic, Two Enumerative Functions
Eric Weisstein's World of Mathematics, Cross Polytope
FORMULA
a(n) = binomial(2*n,4) +binomial(n,2) -n*binomial(2*n-2,2).
a(n) = binomial(n,4)*16. - Zerinvary Lajos, Dec 07 2007
G.f.: 16*x^4/(1-x)^5. - Colin Barker, Apr 14 2012
a(n) = 2*n*(n-1)*(n-2)*(n-3)/3 = 2*A162668(n-3). - Robert Israel, Jul 06 2015
a(n) = 16 * A000332(n). - Alois P. Heinz, Oct 26 2020
MAPLE
a:= n-> binomial(2*n, 4) +binomial(n, 2) -n*binomial(2*n-2, 2);
seq(binomial(n, n-4)*2^4, n=4..37); # Zerinvary Lajos, Dec 07 2007
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Milan Janjic, Jul 16 2007
STATUS
approved