A271617 T(n,k) = 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 k elements linked to themselves.

1, 1, 3, 1, 3, 2, 1, 4, 17, 6, 1, 4, 17, 114, 240, 1, 4, 26, 114, 240, 2238, 1, 4, 26, 307, 2571, 2238, 2196, 1, 4, 27, 307, 2571, 42702, 216318, 37004, 1, 4, 27, 406, 7764, 42702, 216318, 5622392, 20454036, 1, 4, 27, 406, 7764, 222936, 3243689, 5622392, 20454036, 970623228

Offset: 1

Author

R. H. Hardin, Apr 10 2016

Keywords

• nonn
• tabl

Comments

Table starts

........1........1..........1..........1...........1...........1............1

........3........3..........4..........4...........4...........4............4

........2.......17.........17.........26..........26..........27...........27

........6......114........114........307.........307.........406..........406

......240......240.......2571.......2571........7764........7764........12180

.....2238.....2238......42702......42702......222936......222936.......550173

.....2196...216318.....216318....3243689.....3243689....18314708.....18314708

....37004..5622392....5622392..132728354...132728354..1182352612...1182352612

.20454036.20454036.1491326272.1491326272.30892003921.30892003921.291282493174

Examples

			Some solutions for n=4 k=4
.....5........5........0........5........0........6........5........5
....2.0......2.0......0.5......2.0......6.0......5.1......2.0......2.6
...6.6.6....0.5.5....5.2.5....0.0.0....0.1.6....2.0.0....5.4.3....5.5.1
..0.1.1.1..0.2.2.0..2.0.2.0..4.3.4.3..0.4.3.1..0.4.3.0..2.0.4.3..2.2.4.3
Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7
		

Links

• Alois P. Heinz, Antidiagonals n = 1..20, flattened (first 16 antidiagonals from R. H. Hardin)