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A184761 T(n,k)=Half the number of nXk binary arrays with no 1 having an adjacent 1 both above and to its left.

%I A184761 #7 Jul 22 2025 09:42:54
%S A184761 1,2,2,4,7,4,8,25,25,8,16,89,163,89,16,32,317,1056,1056,317,32,64,
%T A184761 1129,6847,12397,6847,1129,64,128,4021,44391,145778,145778,44391,4021,
%U A184761 128,256,14321,287802,1713803,3110914,1713803,287802,14321,256,512,51005,1865917
%N A184761 T(n,k)=Half the number of nXk binary arrays with no 1 having an adjacent 1 both above and to its left.
%C A184761 Table starts
%C A184761 ...1......2........4...........8.............16...............32
%C A184761 ...2......7.......25..........89............317.............1129
%C A184761 ...4.....25......163........1056...........6847............44391
%C A184761 ...8.....89.....1056.......12397.........145778..........1713803
%C A184761 ..16....317.....6847......145778........3110914.........66363023
%C A184761 ..32...1129....44391.....1713803.......66363023.......2568513843
%C A184761 ..64...4021...287802....20148584.....1415755252......99419347147
%C A184761 .128..14321..1865917...236878817....30202770902....3848174315295
%C A184761 .256..51005.12097367..2784890782...644326291402..148949599913987
%C A184761 .512.181657.78431296.32740859687.13745636657969.5765325542821919
%H A184761 R. H. Hardin, <a href="/A184761/b184761.txt">Table of n, a(n) for n = 1..760</a>
%e A184761 Some solutions for 4X3
%e A184761 ..1..1..0....1..0..0....0..1..1....0..0..0....0..0..1....1..0..0....0..0..0
%e A184761 ..0..0..0....0..0..1....0..0..1....0..0..1....1..0..0....0..1..0....1..0..1
%e A184761 ..1..1..0....1..0..1....1..1..0....0..0..1....1..1..0....0..0..1....1..0..1
%e A184761 ..0..0..0....0..0..0....0..0..1....1..1..0....0..1..0....1..0..0....0..1..0
%Y A184761 Column 2 is A007484(n-1) and 1/2 A055099 and 1/4 A104934(n+1)
%K A184761 nonn,tabl
%O A184761 1,2
%A A184761 _R. H. Hardin_ Jan 21 2011