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A326105 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A326105 #4 Jun 06 2019 07:56:52
%S A326105 1,2,2,4,8,4,8,29,29,8,16,108,161,108,16,32,401,929,929,401,32,64,
%T A326105 1490,5383,8628,5383,1490,64,128,5536,31236,81088,81088,31236,5536,
%U A326105 128,256,20569,181227,760989,1233763,760989,181227,20569,256,512,76424,1051456
%N A326105 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A326105 Table starts
%C A326105 ...1.....2.......4.........8..........16............32..............64
%C A326105 ...2.....8......29.......108.........401..........1490............5536
%C A326105 ...4....29.....161.......929........5383.........31236..........181227
%C A326105 ...8...108.....929......8628.......81088........760989.........7140349
%C A326105 ..16...401....5383.....81088.....1233763......18773244.......285501774
%C A326105 ..32..1490...31236....760989....18773244.....463572941.....11436374461
%C A326105 ..64..5536..181227...7140349...285501774...11436374461....457515856087
%C A326105 .128.20569.1051456..67004116..4342306378..282167817331..18304957522469
%C A326105 .256.76424.6100399.628759699.66044562508.6962226034753.732434052866467
%H A326105 R. H. Hardin, <a href="/A326105/b326105.txt">Table of n, a(n) for n = 1..241</a>
%F A326105 Empirical for column k:
%F A326105 k=1: a(n) = 2*a(n-1)
%F A326105 k=2: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3) -a(n-4)
%F A326105 k=3: a(n) = 5*a(n-1) +5*a(n-2) -2*a(n-3) -3*a(n-6) -2*a(n-7) -a(n-8) -a(n-9)
%F A326105 k=4: [order 22]
%F A326105 k=5: [order 59] for n>60
%e A326105 Some solutions for n=5 k=4
%e A326105 ..0..0..1..0. .0..1..1..1. .0..1..1..0. .0..1..0..1. .0..0..0..0
%e A326105 ..1..1..0..0. .0..0..1..1. .1..0..0..1. .0..1..1..0. .1..1..0..1
%e A326105 ..0..1..1..1. .1..0..0..1. .1..1..0..1. .1..0..1..1. .0..1..0..1
%e A326105 ..0..0..1..0. .1..0..1..0. .0..0..0..0. .1..0..0..0. .0..1..0..0
%e A326105 ..1..0..1..0. .1..1..1..0. .1..1..1..1. .1..1..1..1. .0..1..0..0
%Y A326105 Column 1 is A000079(n-1).
%Y A326105 Column 2 is A220547.
%K A326105 nonn,tabl
%O A326105 1,2
%A A326105 _R. H. Hardin_, Jun 06 2019