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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A195971.

Sequence in context: A273096 A076619 A318140 * A216626 A319526 A258835

Adjacent sequences: A266022 A266023 A266024 * A266026 A266027 A266028

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 20 2015

Status

approved