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
Keywords
Examples
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
Formula
a(n) = Sum_{i=0..1} A288852(n,floor(n*(n+1)/4)-i). - Alois P. Heinz, Jun 18 2017
Extensions
a(16)-a(18) from Alois P. Heinz, Jun 15 2017
Comments