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

2,2

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

Formula

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

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

Prog

(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

Crossrefs

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

Sequence in context: A237628 A074043 A120467 * A332961 A012634 A043060

Adjacent sequences: A323496 A323497 A323498 * A323500 A323501 A323502

Keyword

nonn

Author

Eric W. Weisstein, Jan 16 2019

Extensions

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

Status

approved