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

1,3

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

Links

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

Example

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

Crossrefs

Sequence in context: A047787 A102668 A243848 * A057741 A133571 A357059

Adjacent sequences: A271614 A271615 A271616 * A271618 A271619 A271620

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 10 2016

Status

approved