A271612 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 3 elements linked to themselves.

1, 4, 17, 114, 2571, 42702, 216318, 5622392, 1491326272, 101843558868, 1038614548176, 131929454285752, 334070494079203752, 109915013016304822208, 3147612978951707912144, 2069163709506683013857472, 44655320458467210977882177104, 75051772861714827753881814035744

Offset

1,2

Comments

Column 3 of A271617.

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = Sum_{i=0..1} A288852(n,floor(n*(n+1)/4)-i). - Alois P. Heinz, Jun 18 2017

Example

Some solutions for n=4
.....5........5........0........5........6........5........6........5
....2.6......2.5......6.6......2.6......5.1......2.6......0.1......2.5
...0.6.1....5.2.6....5.1.1....4.3.1....2.0.5....0.5.1....4.3.5....6.2.5
..4.3.1.0..2.0.0.1..2.0.4.3..0.0.4.3..4.3.2.0..0.2.4.3..4.3.2.0..0.1.2.0
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: A330514 A330535 A004140 * A240323 A335945 A360879

Adjacent sequences: A271609 A271610 A271611 * A271613 A271614 A271615

Keyword

nonn

Author

R. H. Hardin, Apr 10 2016

Extensions

a(16)-a(18) from Alois P. Heinz, Jun 15 2017

Status

approved