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A263796 Number of (n+1)X(5+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 A263796 #6 Jul 23 2025 15:38:50
%S A263796 4,4,14,17,61,130,494,1435,4917,13962,41366,107284,280438,666212,
%T A263796 1574783,3468753,7560914,15618901,31856173,62297164,120205886,
%U A263796 224230549,412782291,739028663,1306513751,2256420867,3851037496,6442700456
%N A263796 Number of (n+1)X(5+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 A263796 Column 5 of A263799
%H A263796 R. H. Hardin, <a href="/A263796/b263796.txt">Table of n, a(n) for n = 1..210</a>
%F A263796 Empirical: a(n) = a(n-1) +18*a(n-2) -18*a(n-3) -153*a(n-4) +153*a(n-5) +816*a(n-6) -816*a(n-7) -3060*a(n-8) +3060*a(n-9) +8568*a(n-10) -8568*a(n-11) -18564*a(n-12) +18564*a(n-13) +31824*a(n-14) -31824*a(n-15) -43758*a(n-16) +43758*a(n-17) +48620*a(n-18) -48620*a(n-19) -43758*a(n-20) +43758*a(n-21) +31824*a(n-22) -31824*a(n-23) -18564*a(n-24) +18564*a(n-25) +8568*a(n-26) -8568*a(n-27) -3060*a(n-28) +3060*a(n-29) +816*a(n-30) -816*a(n-31) -153*a(n-32) +153*a(n-33) +18*a(n-34) -18*a(n-35) -a(n-36) +a(n-37)
%e A263796 Some solutions for n=5
%e A263796 ..1..1..1..1..0..0....1..1..1..1..0..0....1..1..1..1..0..0....1..1..1..1..1..1
%e A263796 ..1..1..1..1..0..0....1..1..0..0..1..1....1..1..0..0..0..0....1..1..1..1..1..1
%e A263796 ..1..1..1..1..0..0....1..0..1..0..1..0....1..0..1..0..1..0....1..1..1..1..0..0
%e A263796 ..1..1..1..1..0..0....1..0..0..1..0..0....1..0..0..1..1..1....1..1..1..1..0..0
%e A263796 ..1..1..0..0..1..1....0..1..1..0..1..1....0..0..1..0..0..1....1..1..0..0..0..0
%e A263796 ..1..1..0..0..1..1....0..1..0..0..1..0....0..0..0..0..0..0....1..1..0..0..0..0
%Y A263796 Cf. A263799
%K A263796 nonn
%O A263796 1,1
%A A263796 _R. H. Hardin_, Oct 26 2015