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A303421 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303421 #4 Apr 23 2018 10:55:12
%S A303421 1,2,2,4,8,4,8,32,32,8,16,128,252,128,16,32,512,1985,1988,512,32,64,
%T A303421 2048,15647,30897,15684,2048,64,128,8192,123337,480953,480960,123732,
%U A303421 8192,128,256,32768,972168,7486281,14783632,7486369,976132,32768,256,512,131072
%N A303421 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303421 Table starts
%C A303421 ...1......2........4...........8.............16...............32
%C A303421 ...2......8.......32.........128............512.............2048
%C A303421 ...4.....32......252........1985..........15647...........123337
%C A303421 ...8....128.....1988.......30897.........480953..........7486281
%C A303421 ..16....512....15684......480960.......14783632........454377792
%C A303421 ..32...2048...123732.....7486369......454381369......27575294129
%C A303421 ..64...8192...976132...116529645....13965759339....1673515027797
%C A303421 .128..32768..7700788..1813851698...429248347970..101563813268522
%C A303421 .256.131072.60752164.28233652317.13193275586412.6163796529251277
%H A303421 R. H. Hardin, <a href="/A303421/b303421.txt">Table of n, a(n) for n = 1..311</a>
%F A303421 Empirical for column k:
%F A303421 k=1: a(n) = 2*a(n-1)
%F A303421 k=2: a(n) = 4*a(n-1)
%F A303421 k=3: a(n) = 7*a(n-1) +6*a(n-2) +8*a(n-3)
%F A303421 k=4: a(n) = 14*a(n-1) +21*a(n-2) +54*a(n-3) -23*a(n-4) -18*a(n-5) -20*a(n-6)
%F A303421 k=5: [order 16]
%F A303421 k=6: [order 31]
%F A303421 k=7: [order 58]
%F A303421 Empirical for row n:
%F A303421 n=1: a(n) = 2*a(n-1)
%F A303421 n=2: a(n) = 4*a(n-1)
%F A303421 n=3: a(n) = 7*a(n-1) +4*a(n-2) +21*a(n-3) +18*a(n-4)
%F A303421 n=4: [order 9]
%F A303421 n=5: [order 19]
%F A303421 n=6: [order 44]
%e A303421 Some solutions for n=5 k=4
%e A303421 ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..1
%e A303421 ..0..1..0..0. .1..1..1..0. .0..1..0..1. .1..0..1..1. .0..0..0..1
%e A303421 ..1..1..1..0. .0..0..1..0. .0..1..0..1. .0..0..0..0. .1..0..0..0
%e A303421 ..0..0..1..0. .0..1..0..1. .0..0..0..1. .1..1..1..0. .0..1..0..1
%e A303421 ..1..0..0..0. .1..1..0..0. .0..1..1..0. .0..0..0..0. .0..0..1..1
%Y A303421 Column 1 is A000079(n-1).
%Y A303421 Column 2 is A004171(n-1).
%Y A303421 Row 1 is A000079(n-1).
%Y A303421 Row 2 is A004171(n-1).
%K A303421 nonn,tabl
%O A303421 1,2
%A A303421 _R. H. Hardin_, Apr 23 2018