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A301615 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

%I A301615 #4 Mar 24 2018 11:42:37
%S A301615 0,1,1,1,3,1,2,11,11,2,3,34,62,34,3,5,111,367,367,111,5,8,361,2131,
%T A301615 3816,2131,361,8,13,1172,12467,40085,40085,12467,1172,13,21,3809,
%U A301615 72758,421025,758338,421025,72758,3809,21,34,12377,425003,4422826,14345706,14345706
%N A301615 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.
%C A301615 Table starts
%C A301615 ..0.....1.......1.........2...........3..............5................8
%C A301615 ..1.....3......11........34.........111............361.............1172
%C A301615 ..1....11......62.......367........2131..........12467............72758
%C A301615 ..2....34.....367......3816.......40085.........421025..........4422826
%C A301615 ..3...111....2131.....40085......758338.......14345706........271301458
%C A301615 ..5...361...12467....421025....14345706......488491106......16632517333
%C A301615 ..8..1172...72758...4422826...271301458....16632517333....1019565752074
%C A301615 .13..3809..425003..46459647..5131197358...566336198475...62500458737127
%C A301615 .21.12377.2481842.488047397.97045266159.19283659583317.3831336753439723
%H A301615 R. H. Hardin, <a href="/A301615/b301615.txt">Table of n, a(n) for n = 1..220</a>
%F A301615 Empirical for column k:
%F A301615 k=1: a(n) = a(n-1) +a(n-2)
%F A301615 k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F A301615 k=3: [order 10]
%F A301615 k=4: [order 20] for n>21
%F A301615 k=5: [order 68] for n>69
%e A301615 Some solutions for n=5 k=4
%e A301615 ..0..0..0..1. .0..1..0..0. .0..0..0..1. .0..1..1..1. .0..1..0..0
%e A301615 ..1..1..1..1. .0..1..0..0. .0..0..1..1. .0..1..1..1. .0..1..0..1
%e A301615 ..0..1..0..1. .0..0..1..0. .0..0..0..1. .1..0..0..0. .1..1..0..1
%e A301615 ..0..1..0..1. .0..1..1..0. .1..1..1..0. .1..1..1..0. .1..0..0..1
%e A301615 ..1..1..0..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .1..0..0..1
%Y A301615 Column 1 is A000045(n-1).
%Y A301615 Column 2 is A180762.
%K A301615 nonn,tabl
%O A301615 1,5
%A A301615 _R. H. Hardin_, Mar 24 2018