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A265981 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors less than itself. 9

%I

%S 1,3,1,5,23,1,11,117,123,1,26,583,1267,809,1,55,5554,11573,13894,5274,

%T 1,119,52555,320641,282056,262258,33923,1,263,405165,8061815,40743954,

%U 8935989,3699605,219807,1,573,3187023,133236904,3698768651,5155545324

%N T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors less than itself.

%C Table starts

%C .1........3...........5...........11.............26..............55

%C .1.......23.........117..........583...........5554...........52555

%C .1......123........1267........11573.........320641.........8061815

%C .1......809.......13894.......282056.......40743954......3698768651

%C .1.....5274......262258......8935989.....5155545324...1978988798923

%C .1....33923.....3699605....250833288...620145580463.809078767234538

%C .1...219807....50337359...7041080382.79392682076391

%C .1..1424725...795864688.208041110790

%C .1..9226721.11746148349

%C .1.59782080

%H R. H. Hardin, <a href="/A265981/b265981.txt">Table of n, a(n) for n = 1..71</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: [order 15]

%F k=3: [order 35] for n>36

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4)

%F n=2: [order 26]

%e Some solutions for n=3 k=4

%e ..0..4..2..0....0..0..0..1....2..1..4..1....0..0..1..2....2..0..4..1

%e ..1..0..0..3....3..0..6..0....3..0..0..1....0..6..1..3....3..0..0..0

%e ..1..4..2..1....1..2..0..0....2..1..4..1....0..4..0..1....0..0..4..1

%Y Column 2 is A196424.

%Y Row 1 is A196423.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 19 2015

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Last modified July 27 04:55 EDT 2021. Contains 346305 sequences. (Running on oeis4.)