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%I #4 Feb 13 2018 21:01:35
%S 1,2,2,3,1,3,5,3,3,5,8,5,5,5,8,13,8,11,11,8,13,21,15,19,23,19,15,21,
%T 34,26,35,53,53,35,26,34,55,45,65,121,113,121,65,45,55,89,80,120,250,
%U 256,256,250,120,80,89,144,140,220,533,541,576,541,533,220,140,144,233,245
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ..1..2...3....5....8...13....21....34....55.....89....144....233.....377
%C ..2..1...3....5....8...15....26....45....80....140....245....431.....756
%C ..3..3...5...11...19...35....65...120...220....404....744...1369....2517
%C ..5..5..11...23...53..121...250...533..1162...2490...5327..11465...24641
%C ..8..8..19...53..113..256...541..1148..2488...5349..11453..24617...52916
%C .13.15..35..121..256..576..1225..2601..5625..12100..25921..55696..119716
%C .21.26..65..250..541.1225..2583..5488.11899..25570..54750.117697..252985
%C .34.45.120..533.1148.2601..5488.11656.25269..54309.116285.249968..537305
%C .55.80.220.1162.2488.5625.11899.25269.54738.117679.252010.541648.1164265
%H R. H. Hardin, <a href="/A299595/b299595.txt">Table of n, a(n) for n = 1..9934</a>
%F Empirical for diagonal: [linear recurrence of order 15] for n>18
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +2*a(n-3) +a(n-5) for n>6
%F k=3: a(n) = a(n-1) +2*a(n-3) +a(n-4) +a(n-5) for n>8
%F k=4..99: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0
%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..0
%e ..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0
%e ..1..0..0..1. .1..0..0..0. .1..0..0..0. .1..0..0..0. .0..0..0..1
%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0
%Y Column 1 is A000045(n+1).
%Y Column 2 is A193147.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 13 2018
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