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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. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)