A323499 Number of minimum dominating sets in the n-triangular (Johnson) graph.

1, 3, 15, 15, 195, 105, 2625, 945, 38745, 10395, 634095, 135135, 11486475, 2027025, 229053825, 34459425, 4996616625, 654729075, 118505962575, 13749310575, 3038597637075, 316234143225, 83802047954625, 7905853580625, 2474532170735625, 213458046676875

Offset: 2

Author

Eric W. Weisstein, Jan 16 2019

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..200
• Eric Weisstein's World of Mathematics, Johnson Graph
• Eric Weisstein's World of Mathematics, Minimum Dominating Set
• Eric Weisstein's World of Mathematics, Triangular Graph

Crossrefs

Cf. A290716, A290847, A298104, A303048, A303227, A304561.

Programs

PARI

a(n)={my(m=(n+1)\2); ((2*m)!/(m!*2^m))*if(n%2, 1, 1 + n*(n/2-1))} \\ Andrew Howroyd, Sep 08 2019

Formula

a(n) = n!! for n odd.

a(n) = (n-1)!!*(1 + n*(n/2 - 1)) for n even. - Andrew Howroyd, Sep 08 2019

Extensions

Terms a(14) and beyond from Andrew Howroyd, Sep 08 2019