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A130810
If X_1,...,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 4-subsets of X containing none of X_i, (i=1,...,n).
8
16, 80, 240, 560, 1120, 2016, 3360, 5280, 7920, 11440, 16016, 21840, 29120, 38080, 48960, 62016, 77520, 95760, 117040, 141680, 170016, 202400, 239200, 280800, 327600, 380016, 438480, 503440, 575360, 654720, 742016, 837760, 942480, 1056720
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
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
KEYWORD
nonn,easy
AUTHOR
Milan Janjic, Jul 16 2007
STATUS
approved