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%I #4 Dec 28 2017 11:31:24
%S 2,3,4,5,8,8,8,22,21,16,13,53,96,55,32,21,134,334,421,144,64,34,333,
%T 1310,2119,1847,377,128,55,833,4888,13067,13428,8105,987,256,89,2078,
%U 18604,73147,130297,85065,35568,2584,512,144,5190,70255,427900,1091456,1299649
%N T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0 or 2 neighboring 1s.
%C Table starts
%C ...2....3......5........8.........13..........21............34..............55
%C ...4....8.....22.......53........134.........333...........833............2078
%C ...8...21.....96......334.......1310........4888.........18604...........70255
%C ..16...55....421.....2119......13067.......73147........427900.........2455970
%C ..32..144...1847....13428.....130297.....1091456.......9831967........85542000
%C ..64..377...8105....85065....1299649....16277492.....225944546......2976461197
%C .128..987..35568...538819...12964224...242728633....5193690642....103574723331
%C .256.2584.156089..3412881..129324245..3619361855..119391166963...3603917287497
%C .512.6765.684994.21617001.1290083201.53967869192.2744583368968.125396477316407
%H R. H. Hardin, <a href="/A297338/b297338.txt">Table of n, a(n) for n = 1..574</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) -a(n-2)
%F k=3: a(n) = 5*a(n-1) -2*a(n-2) -3*a(n-3)
%F k=4: a(n) = 8*a(n-1) -10*a(n-2) -4*a(n-3) +3*a(n-4) +a(n-5)
%F k=5: [order 7] for n>8
%F k=6: [order 13] for n>14
%F k=7: [order 20] for n>22
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-2)
%F n=2: a(n) = a(n-1) +3*a(n-2) +2*a(n-3) -a(n-5)
%F n=3: [order 12]
%F n=4: [order 31]
%F n=5: [order 82]
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .1..0..0..0. .0..0..1..0. .0..0..1..1. .1..0..1..0
%e ..1..0..1..0. .0..0..1..0. .1..0..0..0. .0..1..1..0. .1..0..0..1
%e ..0..0..1..0. .1..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..1
%e ..0..0..0..1. .1..0..0..1. .0..0..0..1. .0..0..0..1. .1..0..0..0
%e ..0..1..0..0. .1..0..0..1. .0..0..0..0. .1..0..0..1. .1..0..0..0
%Y Column 1 is A000079.
%Y Column 2 is A001906(n+1).
%Y Row 1 is A000045(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 28 2017
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