A297008 Number of edge covers in the complete tripartite graph K_{n,n,n}.

4, 2902, 117207580, 268752741193822, 37231937318464496521924, 323097476641999571450657507823382, 178177528846515370073473806783721111760309500, 6274803675843247716007930604166972482973014660984656159102

Offset: 1

Author

Eric W. Weisstein, Dec 23 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..25
• Eric Weisstein's World of Mathematics, Complete Tripartite Graph
• Eric Weisstein's World of Mathematics, Edge Cover

Crossrefs

Cf. A048291, A183109.

Programs

Mathematica

b[m_, n_] := Sum[(-1)^j*Binomial[m, j]*If[n == 0, 1, (2^(m - j) - 1)^n], {j, 0, m}];
c[n_, s_] := Sum[Binomial[n, k]*Binomial[n, s - k]*b[k, s - k], {k, Max[0, s - n], Min[n, s]}];
a[n_] := Sum[c[n, 2*n - i]*Sum[(-1)^j*Binomial[i, j]*(2^(2*n - j) - 1)^n, {j, 0, i}], {i, 0, 2 n}];
Array[a, 10] (* Jean-François Alcover, Dec 27 2017, after Andrew Howroyd *)

PARI

\\ here b(m,n) is A183109.
b(m, n)={sum(j=0, m, (-1)^j*binomial(m, j)*(2^(m - j) - 1)^n)}
c(n, s)={sum(k=max(0, s-n), min(n, s),binomial(n, k)*binomial(n, s-k)*b(k, s-k))}
a(n)={sum(i=0, 2*n, c(n, 2*n-i)*sum(j=0, i, (-1)^j*binomial(i, j)*(2^(2*n - j) - 1)^n))} \\ Andrew Howroyd, Dec 24 2017

Extensions

Terms a(4) and beyond from Andrew Howroyd, Dec 24 2017