OFFSET
7,1
COMMENTS
Number of n permutations (n>=7) of 3 objects u,v,z, with repetition allowed, containing n-7 u's. Example: if n=7 then n-7 =(0) zero u, a(1)=128. - Zerinvary Lajos, Aug 05 2008
a(n) is the number of 6-dimensional elements in an n-cross polytope where n>=7. - Patrick J. McNab, Jul 06 2015
LINKS
Milan Janjic, Two Enumerative Functions
Eric Weisstein's World of Mathematics, Cross Polytope
FORMULA
a(n) = binomial(2*n,7) + binomial(n,2)*binomial(2*n-4,3) - n*binomial(2*n-2,5) - (2*n-6)*binomial(n,3).
a(n) = C(n,n-7)*2^7, n>=7. - Zerinvary Lajos, Dec 07 2007
G.f.: 128*x^7/(1-x)^8. - Colin Barker, Mar 18 2012
a(n) = 128*A000580(n). a(n+1) = 2*(n+1)*a(n)/(n-6) for n >= 7. - Robert Israel, Jul 08 2015
MAPLE
a:=n->binomial(2*n, 7)+binomial(n, 2)*binomial(2*n-4, 3)-n*binomial(2*n-2, 5)-(2*n-6)*binomial(n, 3);
seq(binomial(n, n-7)*2^7, n=7..32); # Zerinvary Lajos, Dec 07 2007
seq(binomial(n+6, 7)*2^7, n=1..22); # Zerinvary Lajos, Aug 05 2008
MATHEMATICA
Table[Binomial[n, n - 7] 2^7, {n, 7, 40}] (* Vincenzo Librandi, Jul 09 2015 *)
PROG
(Magma) [Binomial(n, n-7)*2^7: n in [7..40]]; // Vincenzo Librandi, Jul 09 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Milan Janjic, Jul 16 2007
STATUS
approved