

A167987


Number of (undirected) cycles in the graph of the northoplex, n>=2.


4



1, 63, 2766, 194650, 21086055, 3257119761, 679314442828, 183842034768036, 62630787876947325, 26224409462275175635, 13236607762537219815546, 7925653200467421739217118, 5554198822066977588903819331, 4503367772662184077396436475525, 4182811121982123218357983540881240
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OFFSET

2,2


COMMENTS

Row sums of triangle in A167986.
The northoplex, also known as the ncrosspolytope, is the dual of the ncube.
A.k.a. number of (undirected) cycles in the ncocktail party graph.  Eric W. Weisstein, Dec 29 2013


LINKS

Andrew Howroyd, Table of n, a(n) for n = 2..100
Eric Weisstein's World of Mathematics, Cocktail Party Graph
Eric Weisstein's World of Mathematics, Cross Polytope
Eric Weisstein's World of Mathematics, Graph Cycle


FORMULA

a(n) = Sum_{k=3..2*n} Sum_{j=0..floor(k/2)} (1)^j*binomial(n,j) * binomial(2*(nj),k2*j) * 2^j*(kj1)!/2.  Andrew Howroyd, May 09 2017


EXAMPLE

a(3) = 63, because in dimension n=3, the orthoplex is the octahedron, which has 63 cycles in its graph.


MATHEMATICA

a[n_] := Sum[Sum[(1)^j*Binomial[n, j]*Binomial[2*(n  j), k  2*j]*2^j*(k  j  1)!, {j, 0, k/2}], {k, 3, 2 n}]/2; Array[a, 15, 2] (* JeanFrançois Alcover, Nov 01 2017, after Andrew Howroyd *)


PROG

(PARI)
a(n)=sum(k=3, 2*n, sum(j=0, k\2, (1)^j*binomial(n, j)*binomial(2*(nj), k2*j)*2^j*(kj1)!))/2; \\ Andrew Howroyd, May 09 2017


CROSSREFS

Cf. A167986.
Sequence in context: A094938 A006110 A132051 * A273437 A069381 A051589
Adjacent sequences: A167984 A167985 A167986 * A167988 A167989 A167990


KEYWORD

nonn


AUTHOR

Andrew Weimholt, Nov 16 2009


EXTENSIONS

a(8)a(11) from Eric W. Weisstein, Dec 19 2013
a(12) from Eric W. Weisstein, Dec 21 2013
a(13) from Eric W. Weisstein, Jan 08 2014
a(14) from Eric W. Weisstein, Apr 09 2014
a(15)a(16) from Andrew Howroyd, May 09 2017


STATUS

approved



