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%I #4 Apr 05 2018 09:38:35
%S 1,2,2,3,3,4,5,11,6,8,8,21,13,10,16,13,31,26,33,21,32,21,113,48,66,58,
%T 42,64,34,363,121,194,153,153,86,128,55,813,275,663,445,380,336,179,
%U 256,89,1751,600,2048,1595,1271,1090,937,370,512,144,5001,1296,5790,4772,5715
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1...2....3....5.....8.....13......21.......34........55.........89
%C ...2...3...11...21....31....113.....363......813......1751.......5001
%C ...4...6...13...26....48....121.....275......600......1296.......2998
%C ...8..10...33...66...194....663....2048.....5790.....17761......58980
%C ..16..21...58..153...445...1595....4772....15249.....49634.....166329
%C ..32..42..153..380..1271...5715...18992....70289....276303....1198933
%C ..64..86..336.1090..3915..18990...76642...360898...1695748....9408402
%C .128.179..937.3120.12420..73663..364922..2150420..13123505...95790405
%C .256.370.2449.9130.42897.312122.1991487.15392485.124691962.1235540899
%H R. H. Hardin, <a href="/A302309/b302309.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F k=3: [order 13] for n>16
%F k=4: [order 60] for n>61
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-2)
%F n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
%F n=3: [order 15] for n>16
%F n=4: [order 61] for n>64
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e ..0..1..0..0. .0..1..0..1. .0..1..1..1. .0..1..0..1. .0..1..0..1
%e ..0..1..0..1. .0..1..0..1. .0..0..0..0. .1..0..0..1. .1..1..0..0
%e ..0..1..0..1. .0..1..0..1. .1..1..1..0. .1..0..1..0. .0..1..0..1
%e ..0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..1..0. .0..1..0..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A240513.
%Y Row 1 is A000045(n+1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Apr 05 2018
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