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A202378 T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 111 in rows and columns.

%I A202378 #7 Jul 22 2025 16:33:48
%S A202378 98,257,257,611,824,611,1326,2293,2293,1326,2815,5677,7349,5677,2815,
%T A202378 5718,13751,20247,20247,13751,5718,11362,31240,54611,62033,54611,
%U A202378 31240,11362,22164,68965,136304,182411,182411,136304,68965,22164,42507,148281
%N A202378 T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 111 in rows and columns.
%C A202378 Table starts
%C A202378 ....98....257.....611.....1326.....2815......5718......11362......22164
%C A202378 ...257....824....2293.....5677....13751.....31240......68965.....148281
%C A202378 ...611...2293....7349....20247....54611....136304.....327679.....763588
%C A202378 ..1326...5677...20247....62033...182411....494783....1285065....3207444
%C A202378 ..2815..13751...54611...182411...589613...1727073....4830102...12936204
%C A202378 ..5718..31240..136304...494783..1727073...5444710...16261405...46335444
%C A202378 .11362..68965..327679..1285065..4830102..16261405...51833855..156557263
%C A202378 .22164.148281..763588..3207444.12936204..46335444..156557263..500733797
%C A202378 .42507.310793.1721033..7727120.33205183.126119710..450660848.1517529198
%C A202378 .80633.640839.3799888.18118987.82794590.331945481.1250551900.4427075014
%H A202378 R. H. Hardin, <a href="/A202378/b202378.txt">Table of n, a(n) for n = 1..261</a>
%e A202378 Some solutions for n=5 k=3
%e A202378 ..0..1..0..1..0....1..1..0..1..0....1..0..1..0..1....1..0..1..0..0
%e A202378 ..1..0..1..0..0....1..0..1..0..0....1..1..0..1..0....1..1..0..0..0
%e A202378 ..0..1..0..0..0....0..1..0..1..0....0..1..0..1..1....0..1..0..0..0
%e A202378 ..1..0..0..0..0....1..1..0..0..0....1..0..0..0..0....1..0..0..0..0
%e A202378 ..1..1..0..0..0....0..0..0..0..0....0..1..0..0..0....0..1..0..0..0
%e A202378 ..0..1..0..0..0....1..1..0..0..0....0..0..0..0..0....1..1..0..0..0
%e A202378 ..0..0..0..0..0....0..1..0..0..0....0..0..0..0..0....1..0..0..0..0
%K A202378 nonn,tabl
%O A202378 1,1
%A A202378 _R. H. Hardin_ Dec 18 2011