cp's OEIS Frontend

A184543 Number of (n+2) X 6 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

%I A184543 #8 Apr 13 2018 08:44:45
%S A184543 220,537,1048,1837,3024,4774,7307,10909,15944,22867,32238,44737,61180,
%T A184543 82536,109945,144737,188452,242861,309988,392133,491896,612202,756327,
%U A184543 927925,1131056,1370215,1650362,1976953,2355972,2793964,3298069,3876057
%N A184543 Number of (n+2) X 6 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.
%C A184543 Column 4 of A184548.
%H A184543 R. H. Hardin, <a href="/A184543/b184543.txt">Table of n, a(n) for n = 1..200</a>
%F A184543 Empirical: a(n) = (1/720)*n^6 + (11/240)*n^5 + (89/144)*n^4 + (209/48)*n^3 + (18317/360)*n^2 + (1231/10)*n + 41.
%F A184543 Conjectures from _Colin Barker_, Apr 13 2018: (Start)
%F A184543 G.f.: x*(220 - 1003*x + 1909*x^2 - 1922*x^3 + 1078*x^4 - 322*x^5 + 41*x^6) / (1 - x)^7.
%F A184543 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A184543 (End)
%e A184543 Some solutions for 4 X 6:
%e A184543 ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..1..1....0..0..0..0..0..1
%e A184543 ..0..0..0..0..0..1....0..0..0..0..0..1....0..0..0..0..1..1....0..0..0..0..0..1
%e A184543 ..0..0..0..0..1..1....0..0..0..1..1..0....0..0..0..1..0..0....1..1..1..1..1..0
%e A184543 ..0..1..1..1..1..0....1..1..1..1..1..0....1..1..1..1..1..1....1..1..1..1..1..0
%Y A184543 Cf. A184548.
%K A184543 nonn
%O A184543 1,1
%A A184543 _R. H. Hardin_, Jan 16 2011