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A263799 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nonincreasing.

%I A263799 #6 Jul 23 2025 15:39:01
%S A263799 2,2,2,3,2,3,3,3,3,3,4,3,7,3,4,4,4,7,7,4,4,5,4,14,7,14,4,5,5,5,14,17,
%T A263799 17,14,5,5,6,5,25,18,61,18,25,5,6,6,6,25,56,130,130,56,25,6,6,7,6,41,
%U A263799 66,494,616,494,66,41,6,7,7,7,41,218,1435,4991,4991,1435,218,41,7,7,8,7,63,272
%N A263799 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nonincreasing.
%C A263799 Table starts
%C A263799 .2.2..3...3.....4.......4........5.........5.........6..........6.........7
%C A263799 .2.2..3...3.....4.......4........5.........5.........6..........6.........7
%C A263799 .3.3..7...7....14......14.......25........25........41.........41........63
%C A263799 .3.3..7...7....17......18.......56........66.......218........272.......798
%C A263799 .4.4.14..17....61.....130......494......1435......4917......13962.....41366
%C A263799 .4.4.14..18...130.....616.....4991.....30130....185795....1022105...5241463
%C A263799 .5.5.25..56...494....4991....62904....760671...8468941...90476206.850301770
%C A263799 .5.5.25..66..1435...30130...760671..20141827.445862545.9910247963
%C A263799 .6.6.41.218..4917..185795..8468941.445862545
%C A263799 .6.6.41.272.13962.1022105.90476206
%H A263799 R. H. Hardin, <a href="/A263799/b263799.txt">Table of n, a(n) for n = 1..144</a>
%F A263799 Empirical for column k:
%F A263799 k=1: a(n) = a(n-1) +a(n-2) -a(n-3)
%F A263799 k=2: a(n) = a(n-1) +a(n-2) -a(n-3)
%F A263799 k=3: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7)
%F A263799 k=4: [order 19]
%F A263799 k=5: [order 37]
%F A263799 k=6: [order 83]
%e A263799 Some solutions for n=5 k=4
%e A263799 ..1..1..0..0..0....1..1..1..1..0....1..1..0..0..0....1..1..0..0..0
%e A263799 ..1..1..0..0..0....1..1..1..1..0....1..1..0..0..0....1..1..0..0..0
%e A263799 ..1..1..0..0..0....1..1..1..1..0....1..1..0..0..0....1..1..0..0..0
%e A263799 ..1..1..0..0..0....1..1..1..1..0....1..1..0..0..0....1..1..0..0..0
%e A263799 ..0..0..1..1..0....1..1..1..1..0....0..0..0..0..0....1..1..0..0..0
%e A263799 ..0..0..1..1..0....1..1..1..1..0....0..0..0..0..0....1..1..0..0..0
%Y A263799 Column 1 is A005578(n+1).
%K A263799 nonn,tabl
%O A263799 1,1
%A A263799 _R. H. Hardin_, Oct 26 2015