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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.

%I A266025 #4 Dec 20 2015 07:13:11
%S A266025 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,
%T A266025 316,259,25,39,719,1045,3796,3796,1045,719,39,64,1784,3394,19688,
%U A266025 39064,19688,3394,1784,64,105,4792,11102,110924,336357,336357,110924,11102,4792,105
%N 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.
%C A266025 Table starts
%C A266025 ...1.....3......4........5..........9...........16...........25............39
%C A266025 ...3.....7.....14.......42.........99..........259..........719..........1784
%C A266025 ...4....14.....33.......91........316.........1045.........3394.........11102
%C A266025 ...5....42.....91......577.......3796........19688.......110924........656555
%C A266025 ...9....99....316.....3796......39064.......336357......3254726......31035211
%C A266025 ..16...259...1045....19688.....336357......4285397.....63460724.....950319651
%C A266025 ..25...719...3394...110924....3254726.....63460724...1577145547...38948760562
%C A266025 ..39..1784..11102...656555...31035211....950319651..38948760562.1561479265416
%C A266025 ..64..4792..36842..3732300..292685424..13831198142.916245375526
%C A266025 .105.12479.122052.21344656.2799525337.203362718849
%H A266025 R. H. Hardin, <a href="/A266025/b266025.txt">Table of n, a(n) for n = 1..127</a>
%F A266025 Empirical for column k:
%F A266025 k=1: a(n) = a(n-1) +a(n-3) +a(n-4)
%F A266025 k=2: [order 21]
%F A266025 k=3: [order 94] for n>95
%e A266025 Some solutions for n=4 k=4
%e A266025 ..1..0..0..1....0..1..2..1....0..1..1..0....0..0..1..2....1..0..1..2
%e A266025 ..1..2..3..2....1..3..2..0....2..1..1..1....0..2..2..1....1..1..3..1
%e A266025 ..1..2..3..1....2..1..2..0....0..1..1..1....1..2..0..2....2..2..2..0
%e A266025 ..0..1..2..0....0..2..1..1....2..1..0..1....1..0..0..1....0..1..2..1
%Y A266025 Column 1 is A195971.
%K A266025 nonn,tabl
%O A266025 1,2
%A A266025 _R. H. Hardin_, Dec 20 2015