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A188992 T(n,k)=Number of nXk binary arrays without the pattern 0 0 1 antidiagonally or horizontally.

%I A188992 #7 Jul 22 2025 11:31:06
%S A188992 2,4,4,7,16,8,12,49,64,16,20,144,295,256,32,33,400,1256,1793,1024,64,
%T A188992 54,1089,5304,10812,10871,4096,128,88,2916,21952,68064,92532,65937,
%U A188992 16384,256,143,7744,89744,423606,852448,791388,399911,65536,512,232,20449
%N A188992 T(n,k)=Number of nXk binary arrays without the pattern 0 0 1 antidiagonally or horizontally.
%C A188992 Table starts
%C A188992 ....2.......4........7.........12...........20.............33...............54
%C A188992 ....4......16.......49........144..........400...........1089.............2916
%C A188992 ....8......64......295.......1256.........5304..........21952............89744
%C A188992 ...16.....256.....1793......10812........68064.........423606..........2613530
%C A188992 ...32....1024....10871......92532.......852448........7844188.........72609144
%C A188992 ...64....4096....65937.....791388.....10682432......144733702.......2002277608
%C A188992 ..128...16384...399911....6768028....133744640.....2668260348......55080396536
%C A188992 ..256...65536..2425505...57879084...1674569728....49183191266....1515192856324
%C A188992 ..512..262144.14710935..494973804..20965958400...906546313088...41677443278252
%C A188992 .1024.1048576.89223345.4232940812.262498839552.16709359181770.1146393385863412
%H A188992 R. H. Hardin, <a href="/A188992/b188992.txt">Table of n, a(n) for n = 1..643</a>
%e A188992 Some solutions for 5X3
%e A188992 ..1..1..1....1..1..0....1..1..1....1..1..1....1..1..1....1..1..1....1..1..0
%e A188992 ..0..1..0....1..0..0....1..0..0....1..1..1....1..1..1....0..1..1....0..1..0
%e A188992 ..1..1..0....0..1..0....1..1..1....1..0..0....0..0..0....1..0..1....0..1..0
%e A188992 ..0..1..1....0..1..1....1..1..0....0..1..0....0..1..1....1..1..1....1..0..1
%e A188992 ..1..1..0....0..1..0....1..1..0....1..0..1....0..0..0....0..1..0....0..1..1
%Y A188992 Column 2 is Column 1 squared
%Y A188992 Row 1 is A000071(n+3)
%Y A188992 Row 2 is A188516
%K A188992 nonn,tabl
%O A188992 1,1
%A A188992 _R. H. Hardin_ Apr 15 2011