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A202202 T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 101 in rows and columns.

%I A202202 #9 Jul 22 2025 16:31:15
%S A202202 108,240,240,450,640,450,756,1400,1400,756,1176,2688,3500,2688,1176,
%T A202202 1728,4704,7560,7560,4704,1728,2430,7680,14700,18144,14700,7680,2430,
%U A202202 3300,11880,26400,38808,38808,26400,11880,3300,4356,17600,44550,76032,90552
%N A202202 T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 101 in rows and columns.
%C A202202 Table starts
%C A202202 ..108...240....450....756....1176....1728.....2430.....3300.....4356......5616
%C A202202 ..240...640...1400...2688....4704....7680....11880....17600....25168.....34944
%C A202202 ..450..1400...3500...7560...14700...26400....44550....71500...110110....163800
%C A202202 ..756..2688...7560..18144...38808...76032...138996...240240...396396....628992
%C A202202 .1176..4704..14700..38808...90552..192192...378378...700700..1233232...2079168
%C A202202 .1728..7680..26400..76032..192192..439296...926640..1830400..3422848...6110208
%C A202202 .2430.11880..44550.138996..378378..926640..2084940..4375800..8664084..16325712
%C A202202 .3300.17600..71500.240240..700700.1830400..4375800..9724000.20323160..40310400
%C A202202 .4356.25168.110110.396396.1233232.3422848..8664084.20323160.44710952..93117024
%C A202202 .5616.34944.163800.628992.2079168.6110208.16325712.40310400.93117024.203164416
%H A202202 R. H. Hardin, <a href="/A202202/b202202.txt">Table of n, a(n) for n = 1..839</a>
%F A202202 Empirical: column k is a polynomial of degree k+2
%F A202202 (via factored column polynomials) T(n,k)=2*(k+2)*(n+2)*product{i=2..k+2 : (n+i) } / n!
%e A202202 Some solutions for n=4 k=3
%e A202202 ..0..1..1..1..1....1..1..0..0..0....0..1..0..0..0....0..1..1..1..0
%e A202202 ..1..1..1..1..1....1..1..1..1..1....1..1..1..1..0....1..1..1..0..0
%e A202202 ..1..1..0..0..0....1..1..1..1..1....1..1..1..0..0....0..0..0..0..0
%e A202202 ..1..1..0..0..0....1..1..1..1..1....1..1..1..0..0....0..0..0..0..0
%e A202202 ..0..1..0..0..0....1..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e A202202 ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%K A202202 nonn,tabl
%O A202202 1,1
%A A202202 _R. H. Hardin_ Dec 14 2011