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A269201 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

%I A269201 #4 Feb 20 2016 10:29:14
%S A269201 4,16,16,60,180,64,216,1284,1740,256,756,9612,25572,15540,1024,2592,
%T A269201 68052,400428,471492,132300,4096,8748,472044,5877228,15289548,8314020,
%U A269201 1090740,16384,29160,3212820,84310620,463790340,555862380,142233732
%N A269201 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.
%C A269201 Table starts
%C A269201 .......4.........16.............60...............216..................756
%C A269201 ......16........180...........1284..............9612................68052
%C A269201 ......64.......1740..........25572............400428..............5877228
%C A269201 .....256......15540.........471492..........15289548............463790340
%C A269201 ....1024.....132300........8314020.........555862380..........34838403756
%C A269201 ....4096....1090740......142233732.......19558138380........2532677348772
%C A269201 ...16384....8787660.....2380537188......672230393004......179867149105740
%C A269201 ...65536...69580980....39186271044....22702294138188....12551707872624132
%C A269201 ..262144..543538380...636703584804...756261535626732...864008559706781292
%C A269201 .1048576.4200069300.10237337586180.24917784636315276.58827234014669683044
%H A269201 R. H. Hardin, <a href="/A269201/b269201.txt">Table of n, a(n) for n = 1..161</a>
%F A269201 Empirical for column k:
%F A269201 k=1: a(n) = 4*a(n-1)
%F A269201 k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3
%F A269201 k=3: a(n) = 30*a(n-1) -237*a(n-2) +180*a(n-3) -36*a(n-4) for n>5
%F A269201 k=4: [order 6] for n>7
%F A269201 k=5: [order 20] for n>21
%F A269201 k=6: [order 42] for n>43
%F A269201 Empirical for row n:
%F A269201 n=1: a(n) = 6*a(n-1) -9*a(n-2)
%F A269201 n=2: a(n) = 10*a(n-1) -13*a(n-2) -60*a(n-3) -36*a(n-4)
%F A269201 n=3: [order 8]
%F A269201 n=4: [order 20]
%F A269201 n=5: [order 52] for n>53
%e A269201 Some solutions for n=3 k=4
%e A269201 ..2..2..0..0. .2..2..1..1. .2..0..0..1. .0..0..2..2. .2..2..2..2
%e A269201 ..1..0..0..2. .2..0..0..0. .0..2..0..2. .2..2..2..2. .0..0..0..1
%e A269201 ..2..0..2..0. .1..0..0..0. .1..0..2..0. .1..0..0..2. .1..1..1..1
%Y A269201 Column 1 is A000302.
%Y A269201 Column 2 is A269103.
%Y A269201 Row 1 is A120926(n+1).
%K A269201 nonn,tabl
%O A269201 1,1
%A A269201 _R. H. Hardin_, Feb 20 2016