A130812 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 6-subsets of X containing none of X_i, (i=1,...n).

64, 448, 1792, 5376, 13440, 29568, 59136, 109824, 192192, 320320, 512512, 792064, 1188096, 1736448, 2480640, 3472896, 4775232, 6460608, 8614144, 11334400, 14734720, 18944640, 24111360, 30401280, 38001600, 47121984, 57996288, 70884352, 86073856, 103882240

Offset

6,1

Comments

Number of n permutations (n>=6) of 3 objects u,v,z, with repetition allowed, containing n-6 u's. Example: if n=6 then n-6 =(0) zero u, a(1)=64. - Zerinvary Lajos, Aug 05 2008

a(n) is the number of 5-dimensional elements in an n-cross polytope where n>=6. - Patrick J. McNab, Jul 06 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 6..1000

Milan Janjic, Two Enumerative Functions

Eric Weisstein's World of Mathematics, Cross Polytope

Formula

a(n) = binomial(2*n,6) + binomial(n,2)*binomial(2*n-4,2) - n*binomial(2*n-2,4) - binomial(n,3).

a(n) = C(n,n-6)*2^6, n>=6. - Zerinvary Lajos, Dec 07 2007

G.f.: 64*x^6/(1-x)^7. - Colin Barker, Mar 20 2012

Maple

a:=n->binomial(2*n, 6)+binomial(n, 2)*binomial(2*n-4, 2)-n*binomial(2*n-2, 4)-binomial(n, 3);
seq(binomial(n, n-6)*2^6, n=6..32); # Zerinvary Lajos, Dec 07 2007
seq(binomial(n+5, 6)*2^6, n=1..22); # Zerinvary Lajos, Aug 05 2008

Mathematica

CoefficientList[Series[64/(1-x)^7, {x, 0, 30}], x] (* Vincenzo Librandi, Mar 21 2012 *)

Prog

(Magma) [Binomial(2*n, 6)+Binomial(n, 2)*Binomial(2*n-4, 2)- n*Binomial(2*n-2, 4)-Binomial(n, 3): n in [6..40]]; // Vincenzo Librandi, Jul 09 2015

Crossrefs

Cf. A038207, A000079, A001787, A001788, A001789, A003472, A054849, A002409, A054851, A140325, A140354, A046092, A130809, A130810, A130811. - Zerinvary Lajos, Aug 05 2008

Sequence in context: A188821 A181210 A092211 * A187518 A221070 A297844

Adjacent sequences: A130809 A130810 A130811 * A130813 A130814 A130815

Keyword

nonn,easy

Author

Milan Janjic, Jul 16 2007

Status

approved