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A301450 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A301450 #4 Mar 21 2018 11:56:38
%S A301450 1,2,2,4,8,4,8,29,29,8,16,108,171,108,16,32,401,1008,1008,401,32,64,
%T A301450 1490,5930,9541,5930,1490,64,128,5536,34976,91370,91370,34976,5536,
%U A301450 128,256,20569,206266,877044,1423344,877044,206266,20569,256,512,76424,1216562
%N A301450 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A301450 Table starts
%C A301450 ...1.....2.......4.........8..........16............32...............64
%C A301450 ...2.....8......29.......108.........401..........1490.............5536
%C A301450 ...4....29.....171......1008........5930.........34976...........206266
%C A301450 ...8...108....1008......9541.......91370........877044..........8414314
%C A301450 ..16...401....5930.....91370.....1423344......22207589........346263718
%C A301450 ..32..1490...34976....877044....22207589.....564002959......14319674594
%C A301450 ..64..5536..206266...8414314...346263718...14319674594.....592006690060
%C A301450 .128.20569.1216562..80726964..5399605493..363595763125...24472344492129
%C A301450 .256.76424.7175157.774477323.84198470831.9231743942243.1011614229196954
%H A301450 R. H. Hardin, <a href="/A301450/b301450.txt">Table of n, a(n) for n = 1..199</a>
%F A301450 Empirical for column k:
%F A301450 k=1: a(n) = 2*a(n-1)
%F A301450 k=2: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3) -a(n-4)
%F A301450 k=3: [order 13]
%F A301450 k=4: [order 40]
%e A301450 Some solutions for n=5 k=4
%e A301450 ..0..0..0..1. .0..1..1..1. .0..1..0..1. .0..1..1..1. .0..0..0..1
%e A301450 ..1..0..1..0. .0..1..0..0. .1..0..1..0. .1..0..0..0. .0..1..0..0
%e A301450 ..1..0..1..1. .1..0..0..0. .0..1..0..1. .1..0..1..1. .1..1..0..1
%e A301450 ..0..1..0..1. .1..1..0..1. .0..0..1..0. .1..0..1..0. .0..1..0..1
%e A301450 ..1..1..0..0. .1..1..0..1. .0..1..1..1. .1..0..0..1. .1..1..0..1
%Y A301450 Column 1 is A000079(n-1).
%Y A301450 Column 2 is A220547.
%K A301450 nonn,tabl
%O A301450 1,2
%A A301450 _R. H. Hardin_, Mar 21 2018