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A318343 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A318343 #4 Aug 24 2018 11:04:59
%S A318343 1,2,2,4,6,4,8,10,10,8,16,20,20,20,16,32,42,36,36,42,32,64,89,76,67,
%T A318343 76,89,64,128,190,160,148,148,160,190,128,256,407,344,343,393,343,344,
%U A318343 407,256,512,873,748,817,1115,1115,817,748,873,512,1024,1874,1624,1975,3321
%N A318343 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A318343 Table starts
%C A318343 ...1...2....4....8....16.....32......64......128.......256........512
%C A318343 ...2...6...10...20....42.....89.....190......407.......873.......1874
%C A318343 ...4..10...20...36....76....160.....344......748......1624.......3544
%C A318343 ...8..20...36...67...148....343.....817.....1975......4788......11644
%C A318343 ..16..42...76..148...393...1115....3321....10111.....30943......95244
%C A318343 ..32..89..160..343..1115...4133...16267....66070....270320....1112195
%C A318343 ..64.190..344..817..3321..16267...86487...476348...2647555...14797928
%C A318343 .128.407..748.1975.10111..66070..476348..3590263..27322989..209259065
%C A318343 .256.873.1624.4788.30943.270320.2647555.27322989.285034170.2994059337
%H A318343 R. H. Hardin, <a href="/A318343/b318343.txt">Table of n, a(n) for n = 1..611</a>
%F A318343 Empirical for column k:
%F A318343 k=1: a(n) = 2*a(n-1)
%F A318343 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-4) for n>6
%F A318343 k=3: a(n) = 2*a(n-1) +2*a(n-2) -3*a(n-3) -2*a(n-4) +2*a(n-5) for n>6
%F A318343 k=4: [order 8] for n>9
%F A318343 k=5: [order 15] for n>18
%F A318343 k=6: [order 23] for n>27
%F A318343 k=7: [order 36] for n>41
%e A318343 Some solutions for n=5 k=4
%e A318343 ..0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A318343 ..1..1..0..0. .1..1..1..1. .0..1..0..0. .0..0..0..0. .1..1..1..1
%e A318343 ..1..0..0..1. .1..1..1..0. .0..0..1..0. .1..1..1..1. .1..1..1..1
%e A318343 ..0..0..1..1. .1..1..0..0. .0..0..0..0. .1..1..1..0. .1..1..1..0
%e A318343 ..0..1..1..0. .1..0..0..1. .0..0..0..1. .1..1..0..0. .1..1..0..0
%Y A318343 Column 1 is A000079(n-1).
%Y A318343 Column 2 is A317759.
%K A318343 nonn,tabl
%O A318343 1,2
%A A318343 _R. H. Hardin_, Aug 24 2018