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

1,2

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.

Links

Table of n, a(n) for n=1..19.

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

Formula

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

Example

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

Crossrefs

Cf. A271617, A288852.

Sequence in context: A086550 A266239 A018864 * A019951 A019971 A330501

Adjacent sequences: A271607 A271608 A271609 * A271611 A271612 A271613

Keyword

nonn

Author

R. H. Hardin, Apr 10 2016

Extensions

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

Status

approved