A271610 Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than 1 elements linked to themselves.

1, 3, 2, 6, 240, 2238, 2196, 37004, 20454036, 970623228, 2317631400, 216893681800, 1257138602103744, 316487245419538728, 2326335506123418128, 1208982377794384163088, 63184698521304672890081520, 85953148896748583125564477008, 2220650888749669503773432361504

Offset: 1

Author

R. H. Hardin, Apr 10 2016

Keywords

• nonn

Comments

In other words, the number of maximum matchings in the (n-1)-triangular grid graph. - Eric W. Weisstein, Jun 14 2017

Column 1 of A271617.

Examples

			All solutions for n=4
.....6........5........6........6........5........5
....5.1......2.6......5.1......6.1......2.5......2.6
...2.6.6....5.5.1....2.4.3....5.1.6....5.2.6....4.3.1
Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7
		

Links

• Eric Weisstein's World of Mathematics, Matching
• Eric Weisstein's World of Mathematics, Maximum Independent Edge Set
• Eric Weisstein's World of Mathematics, Triangular Grid Graph

Crossrefs

Cf. A271617, A288852.

Formula

a(n) = A288852(n,floor(n*(n+1)/4)). - Alois P. Heinz, Jun 18 2017

Extensions

a(16)-a(19) from Alois P. Heinz, Jun 15 2017