A266025 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal, vertical and antidiagonal neighbors exactly one smaller than itself.

1, 3, 3, 4, 7, 4, 5, 14, 14, 5, 9, 42, 33, 42, 9, 16, 99, 91, 91, 99, 16, 25, 259, 316, 577, 316, 259, 25, 39, 719, 1045, 3796, 3796, 1045, 719, 39, 64, 1784, 3394, 19688, 39064, 19688, 3394, 1784, 64, 105, 4792, 11102, 110924, 336357, 336357, 110924, 11102, 4792, 105

Offset: 1

Author

R. H. Hardin, Dec 20 2015

Keywords

• nonn
• tabl

Comments

Table starts

...1.....3......4........5..........9...........16...........25............39

...3.....7.....14.......42.........99..........259..........719..........1784

...4....14.....33.......91........316.........1045.........3394.........11102

...5....42.....91......577.......3796........19688.......110924........656555

...9....99....316.....3796......39064.......336357......3254726......31035211

..16...259...1045....19688.....336357......4285397.....63460724.....950319651

..25...719...3394...110924....3254726.....63460724...1577145547...38948760562

..39..1784..11102...656555...31035211....950319651..38948760562.1561479265416

..64..4792..36842..3732300..292685424..13831198142.916245375526

.105.12479.122052.21344656.2799525337.203362718849

Examples

			Some solutions for n=4 k=4
..1..0..0..1....0..1..2..1....0..1..1..0....0..0..1..2....1..0..1..2
..1..2..3..2....1..3..2..0....2..1..1..1....0..2..2..1....1..1..3..1
..1..2..3..1....2..1..2..0....0..1..1..1....1..2..0..2....2..2..2..0
..0..1..2..0....0..2..1..1....2..1..0..1....1..0..0..1....0..1..2..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..127

Crossrefs

Column 1 is A195971.

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-3) +a(n-4)

k=2: [order 21]

k=3: [order 94] for n>95