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A302741 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302741 #4 Apr 12 2018 11:21:48
%S A302741 1,2,2,4,8,4,8,32,32,8,16,128,228,128,16,32,512,1637,1652,512,32,64,
%T A302741 2048,11814,21625,11980,2048,64,128,8192,85268,285613,286631,86916,
%U A302741 8192,128,256,32768,615589,3778433,6947036,3798398,630604,32768,256,512,131072
%N A302741 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302741 Table starts
%C A302741 ...1......2........4..........8............16..............32
%C A302741 ...2......8.......32........128...........512............2048
%C A302741 ...4.....32......228.......1637.........11814...........85268
%C A302741 ...8....128.....1652......21625........285613.........3778433
%C A302741 ..16....512....11980.....286631.......6947036.......168799572
%C A302741 ..32...2048....86916....3798398.....168833401......7530280825
%C A302741 ..64...8192...630604...50347423....4104946296....336148647504
%C A302741 .128..32768..4575332..667361051...99807877377..15005851329729
%C A302741 .256.131072.33196332.8845980434.2426739457531.669868217032865
%H A302741 R. H. Hardin, <a href="/A302741/b302741.txt">Table of n, a(n) for n = 1..180</a>
%F A302741 Empirical for column k:
%F A302741 k=1: a(n) = 2*a(n-1)
%F A302741 k=2: a(n) = 4*a(n-1)
%F A302741 k=3: a(n) = 7*a(n-1) +2*a(n-2) +2*a(n-3) -20*a(n-4) -16*a(n-5)
%F A302741 k=4: [order 15]
%F A302741 k=5: [order 46]
%F A302741 Empirical for row n:
%F A302741 n=1: a(n) = 2*a(n-1)
%F A302741 n=2: a(n) = 4*a(n-1)
%F A302741 n=3: a(n) = 7*a(n-1) +4*a(n-2) -17*a(n-3) -3*a(n-4) -9*a(n-6) +14*a(n-7) for n>8
%F A302741 n=4: [order 15] for n>16
%F A302741 n=5: [order 64] for n>65
%e A302741 Some solutions for n=5 k=4
%e A302741 ..0..0..1..0. .0..0..1..0. .0..0..1..0. .0..0..0..1. .0..0..1..0
%e A302741 ..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..1. .0..1..0..1
%e A302741 ..0..1..1..1. .0..1..1..0. .0..1..1..1. .0..1..0..0. .0..0..1..0
%e A302741 ..1..0..0..0. .1..1..0..1. .0..0..1..0. .1..1..0..0. .1..1..1..1
%e A302741 ..0..0..1..0. .1..1..0..1. .0..0..1..1. .0..1..1..1. .1..1..0..0
%Y A302741 Column 1 is A000079(n-1).
%Y A302741 Column 2 is A004171(n-1).
%Y A302741 Row 1 is A000079(n-1).
%Y A302741 Row 2 is A004171(n-1).
%K A302741 nonn,tabl
%O A302741 1,2
%A A302741 _R. H. Hardin_, Apr 12 2018