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A266131 T(n,k) = Number of n X k integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors exactly one smaller than itself.

%I A266131 #6 Apr 11 2022 13:18:29
%S A266131 1,3,1,4,9,1,5,25,20,1,9,49,77,61,1,16,149,117,385,189,1,25,625,278,
%T A266131 572,2099,544,1,39,2141,1959,3851,4336,9083,1629,1,64,5433,11044,
%U A266131 44623,62104,19750,48188,4973,1,105,17269,36730,347576,1285961,326145,102201,249446
%N A266131 T(n,k) = Number of n X k integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors exactly one smaller than itself.
%C A266131 Table starts
%C A266131 .1.....3.......4........5.........9.........16..........25.........39
%C A266131 .1.....9......25.......49.......149........625........2141.......5433
%C A266131 .1....20......77......117.......278.......1959.......11044......36730
%C A266131 .1....61.....385......572......3851......44623......347576....1650710
%C A266131 .1...189....2099.....4336.....62104....1285961....16386099..124675418
%C A266131 .1...544....9083....19750....326145...13689944...325554385.3901509248
%C A266131 .1..1629...48188...102201...4176690..311260836.10444421518
%C A266131 .1..4973..249446...620508..50677045.6688962679
%C A266131 .1.15040.1166325..3041449.367191341
%C A266131 .1.45739.6288299.16217839
%H A266131 R. H. Hardin, <a href="/A266131/b266131.txt">Table of n, a(n) for n = 1..97</a>
%F A266131 Empirical for column k:
%F A266131 k=1: a(n) = a(n-1),
%F A266131 k=2: [order 10],
%F A266131 k=3: [order 26] for n>27,
%F A266131 Empirical for row n:
%F A266131 n=1: a(n) = a(n-1) +a(n-3) +a(n-4),
%F A266131 n=2: [order 17],
%F A266131 n=3: [order 77].
%e A266131 Some solutions for n=4, k=4
%e A266131 ..0..0..1..1....0..2..1..2....1..0..2..1....2..1..2..0....0..2..1..0
%e A266131 ..0..2..0..1....0..0..1..2....0..2..0..1....0..1..2..0....0..2..1..1
%e A266131 ..0..0..1..2....0..2..0..2....3..2..1..1....1..0..2..0....0..2..0..2
%e A266131 ..0..2..1..2....0..0..1..1....0..2..1..0....1..1..0..0....0..0..1..1
%Y A266131 Column 2 is A196212.
%Y A266131 Row 1 is A195971.
%K A266131 nonn,tabl
%O A266131 1,2
%A A266131 _R. H. Hardin_, Dec 21 2015