A137886 Number of (directed) Hamiltonian paths in the n-crown graph.
12, 144, 3840, 138240, 6804000, 436504320, 35417088000, 3546005299200, 429451518988800, 61883150757120000, 10463789706751180800, 2051763183437532364800, 461802751261297205760000, 118254166096501129863168000
Offset: 3
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 3..253 (terms 3..50 from Andrew Howroyd)
- Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems
- Eric Weisstein's World of Mathematics, Crown Graph
- Eric Weisstein's World of Mathematics, Hamiltonian Path
Programs
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Mathematica
Table[2 n! Sum[(-1)^(n - k) k! Binomial[n + k, 2 k], {k, 0, n}], {n, 3, 20}] (* Eric W. Weisstein, Sep 20 2017 *) Table[2 (-1)^n n! HypergeometricPFQ[{1, -n, n + 1}, {1/2}, 1/4], {n, 3, 20}] (* Eric W. Weisstein, Sep 20 2017 *) -
PARI
/* needs the routine nhp() from the Alekseyev link */ { A137886(n) = nhp( matrix(2*n,2*n,i,j, if(min(i,j)<=n && max(i,j)>n && abs(j-i)!=n, 1, 0)) ) }
Formula
a(n) ~ 4*Pi*n^(2*n+1) / exp(2*n+2). - Vaclav Kotesovec, Feb 25 2016
a(n) = (n-1)*n*a(n-1) + (n-1)^2*n*a(n-2) + (n-2)*(n-1)*n*a(n-3). - Vaclav Kotesovec, Feb 25 2016
a(n) = 2*n! * A000271(n). - Andrew Howroyd, Sep 19 2017
Extensions
More terms from Max Alekseyev, Feb 13 2009
a(14) from Eric W. Weisstein, Jan 15 2014
a(15)-a(16) from Andrew Howroyd, Feb 21 2016
Comments