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A303242 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303242 #4 Apr 20 2018 10:55:35
%S A303242 1,1,2,1,2,4,1,11,2,8,1,13,18,3,16,1,34,8,55,6,32,1,65,60,10,181,10,
%T A303242 64,1,123,56,255,61,494,21,128,1,266,236,149,1106,160,1465,42,256,1,
%U A303242 499,428,1676,1373,5158,458,4415,86,512,1,1037,1248,3307,11111,7823,23995,1748
%N A303242 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303242 Table starts
%C A303242 ...1..1.....1....1......1.......1........1.........1..........1............1
%C A303242 ...2..2....11...13.....34......65......123.......266........499.........1037
%C A303242 ...4..2....18....8.....60......56......236.......428.......1248.........3264
%C A303242 ...8..3....55...10....255.....149.....1676......3307......18505........65498
%C A303242 ..16..6...181...61...1106....1373....11111.....38480.....221943......1162591
%C A303242 ..32.10...494..160...5158....7823....90728....421983....3251872.....23282610
%C A303242 ..64.21..1465..458..23995...41878...686376...4288552...44547581....435326091
%C A303242 .128.42..4415.1748.108726..277018..5320294..48315454..648070597...8762716079
%C A303242 .256.86.12934.6056.506416.1721671.42575026.536745912.9508520220.176408218876
%H A303242 R. H. Hardin, <a href="/A303242/b303242.txt">Table of n, a(n) for n = 1..199</a>
%F A303242 Empirical for column k:
%F A303242 k=1: a(n) = 2*a(n-1)
%F A303242 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A303242 k=3: [order 13]
%F A303242 k=4: [order 71] for n>72
%F A303242 Empirical for row n:
%F A303242 n=1: a(n) = a(n-1)
%F A303242 n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
%F A303242 n=3: [order 20]
%F A303242 n=4: [order 67] for n>68
%e A303242 Some solutions for n=5 k=4
%e A303242 ..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..1..1. .0..0..1..1
%e A303242 ..0..0..1..1. .1..0..0..0. .1..1..1..0. .0..1..1..0. .0..0..1..1
%e A303242 ..0..0..1..0. .1..0..1..0. .1..1..1..1. .0..1..1..1. .0..1..1..0
%e A303242 ..0..0..1..1. .1..0..0..0. .1..1..1..1. .0..1..1..1. .0..0..1..1
%e A303242 ..0..0..1..1. .0..0..0..1. .0..1..1..0. .0..1..1..0. .0..0..1..1
%Y A303242 Column 1 is A000079(n-1).
%Y A303242 Column 2 is A240513(n-2).
%Y A303242 Row 2 is A297870(n+2).
%K A303242 nonn,tabl
%O A303242 1,3
%A A303242 _R. H. Hardin_, Apr 20 2018