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A301662 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.

%I A301662 #4 Mar 25 2018 11:29:07
%S A301662 1,2,2,3,3,3,5,4,4,5,8,6,6,6,8,13,9,9,9,9,13,21,14,15,13,15,14,21,34,
%T A301662 22,26,24,24,26,22,34,55,35,46,45,46,45,46,35,55,89,56,83,89,99,99,89,
%U A301662 83,56,89,144,90,151,182,223,254,223,182,151,90,144,233,145,276,373,528,696
%N A301662 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.
%C A301662 Table starts
%C A301662 ..1..2...3...5....8...13....21.....34......55......89......144.......233
%C A301662 ..2..3...4...6....9...14....22.....35......56......90......145.......234
%C A301662 ..3..4...6...9...15...26....46.....83.....151.....276......506.......929
%C A301662 ..5..6...9..13...24...45....89....182.....373.....773.....1604......3333
%C A301662 ..8..9..15..24...46...99...223....528....1268....3085.....7557.....18564
%C A301662 .13.14..26..45...99..254...696...2013....5953...17878....54126....164525
%C A301662 .21.22..46..89..223..696..2335...8380...31001..116558...442314...1686894
%C A301662 .34.35..83.182..528.2013..8380..37679..175638..833737..4001569..19319239
%C A301662 .55.56.151.373.1268.5953.31001.175638.1036686.6245327.38085186.233683529
%H A301662 R. H. Hardin, <a href="/A301662/b301662.txt">Table of n, a(n) for n = 1..544</a>
%F A301662 Empirical for column k:
%F A301662 k=1: a(n) = a(n-1) +a(n-2)
%F A301662 k=2: a(n) = 2*a(n-1) -a(n-3)
%F A301662 k=3: a(n) = 2*a(n-1) -a(n-4)
%F A301662 k=4: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A301662 k=5: [order 11]
%F A301662 k=6: [order 18]
%F A301662 k=7: [order 31]
%e A301662 Some solutions for n=5 k=4
%e A301662 ..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A301662 ..1..1..0..1. .1..0..1..0. .1..1..1..0. .1..0..1..0. .1..0..1..0
%e A301662 ..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..1
%e A301662 ..1..1..0..1. .1..1..1..0. .1..0..0..0. .0..1..0..1. .1..0..1..0
%e A301662 ..0..0..1..0. .0..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1
%Y A301662 Column 1 is A000045(n+1).
%Y A301662 Column 2 is A001611(n+1).
%K A301662 nonn,tabl
%O A301662 1,2
%A A301662 _R. H. Hardin_, Mar 25 2018