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A301790 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.

%I A301790 #4 Mar 26 2018 16:42:01
%S A301790 1,2,2,3,5,4,5,6,13,8,8,9,12,34,16,13,14,17,24,89,32,21,22,25,32,48,
%T A301790 233,64,34,35,38,45,61,96,610,128,55,56,59,66,82,116,192,1597,256,89,
%U A301790 90,93,100,116,150,221,384,4181,512,144,145,148,155,171,205,275,421,768,10946
%N A301790 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
%C A301790 Table starts
%C A301790 ...1....2...3...5...8...13...21...34...55...89..144...233...377...610...987
%C A301790 ...2....5...6...9..14...22...35...56...90..145..234...378...611...988..1598
%C A301790 ...4...13..12..17..25...38...59...93..148..237..381...614...991..1601..2588
%C A301790 ...8...34..24..32..45...66..100..155..244..388..621...998..1608..2595..4192
%C A301790 ..16...89..48..61..82..116..171..260..404..637.1014..1624..2611..4208..6792
%C A301790 ..32..233..96.116.150..205..294..438..671.1048.1658..2645..4242..6826.11007
%C A301790 ..64..610.192.221.275..364..508..741.1118.1728.2715..4312..6896.11077.17842
%C A301790 .128.1597.384.421.505..648..881.1258.1868.2855.4452..7036.11217.17982.28928
%C A301790 .256.4181.768.802.928.1156.1532.2142.3129.4726.7310.11491.18256.29202.46913
%H A301790 R. H. Hardin, <a href="/A301790/b301790.txt">Table of n, a(n) for n = 1..1920</a>
%F A301790 Empirical for column k:
%F A301790 k=1: a(n) = 2*a(n-1)
%F A301790 k=2: a(n) = 3*a(n-1) -a(n-2)
%F A301790 k=3: a(n) = 2*a(n-1)
%F A301790 k=4: a(n) = a(n-1) +2*a(n-2) -a(n-4)
%F A301790 k=5: a(n) = 2*a(n-1) -a(n-4)
%F A301790 k=6: a(n) = a(n-1) +2*a(n-2) -a(n-4) -a(n-5) -a(n-6)
%F A301790 k=7: a(n) = 2*a(n-1) -a(n-4) -a(n-6)
%F A301790 Empirical for row n:
%F A301790 n=1: a(n) = a(n-1) +a(n-2)
%F A301790 n=2: a(n) = 2*a(n-1) -a(n-3) for n>5
%F A301790 n=3: a(n) = 2*a(n-1) -a(n-3) for n>5
%F A301790 n=4: a(n) = 2*a(n-1) -a(n-3) for n>5
%F A301790 n=5: a(n) = 2*a(n-1) -a(n-3) for n>5
%F A301790 n=6: a(n) = 2*a(n-1) -a(n-3) for n>6
%F A301790 n=7: a(n) = 2*a(n-1) -a(n-3) for n>7
%e A301790 Some solutions for n=5 k=4
%e A301790 ..0..0..1..0. .0..1..0..1. .0..1..1..0. .0..1..1..0. .0..0..1..0
%e A301790 ..1..0..1..1. .0..1..0..0. .0..0..1..0. .0..0..1..0. .1..0..1..1
%e A301790 ..1..0..0..1. .0..1..1..0. .1..0..1..0. .1..0..1..1. .1..0..0..1
%e A301790 ..1..1..0..0. .0..0..1..0. .0..1..0..1. .1..0..0..1. .1..1..0..1
%e A301790 ..0..1..1..0. .1..0..1..0. .0..1..0..0. .1..1..0..1. .0..1..0..0
%Y A301790 Column 1 is A000079(n-1).
%Y A301790 Column 2 is A001519(n+1).
%Y A301790 Column 3 is A003945.
%Y A301790 Row 1 is A000045(n+1).
%K A301790 nonn,tabl
%O A301790 1,2
%A A301790 _R. H. Hardin_, Mar 26 2018