A214384 T(n,k)=Number of nXnXn triangular 0..k arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors

2, 3, 4, 4, 14, 8, 5, 32, 94, 16, 6, 60, 456, 890, 32, 7, 100, 1506, 11048, 11700, 64, 8, 154, 3976, 74260, 445024, 211760, 128, 9, 224, 9044, 350232, 6981540, 29456216, 5247716, 256, 10, 312, 18480, 1305392, 65905056, 1232720402, 3183854216, 177440488, 512

Offset

1,1

Comments

Table starts

..2.....3......4.......5........6.........7..........8...........9..........10

..4....14.....32......60......100.......154........224.........312.........420

..8....94....456....1506.....3976......9044......18480.......34812.......61512

.16...890..11048...74260...350232...1305392....4107248....11363940....28412824

.32.11700.445024.6981540.65905056.444106514.2347567992.10319444960.39220393240

Links

R. H. Hardin, Table of n, a(n) for n = 1..98

Formula

Empirical: rows n=1..5 are polynomials of degree n(n+1)/2 in k

Example

Some solutions for n=3 k=3
....1......1......1......3......1......3......1......1......2......1......3
...2.1....1.2....1.2....3.1....1.2....1.3....2.0....1.0....1.3....1.0....3.1
..0.2.0..1.3.1..0.2.1..2.3.0..1.2.3..2.1.3..3.0.3..1.2.0..2.1.3..0.1.0..3.0.2

Crossrefs

Row 2 is A159920(n+1)

Sequence in context: A265534 A214554 A185417 * A118022 A181368 A037848

Adjacent sequences: A214381 A214382 A214383 * A214385 A214386 A214387

Keyword

nonn,tabl

Author

R. H. Hardin Jul 14 2012

Status

approved