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A227162 Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order.

%I A227162 #7 Sep 07 2018 08:26:56
%S A227162 4,18,62,193,558,1507,3828,9149,20609,43918,88960,172130,319637,
%T A227162 572050,990413,1664308,2722302,4345275,6783191,10375943,15578976,
%U A227162 22994469,33408938,47838207,67580783,94280764,130001506,177311376,239383023
%N A227162 Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order.
%H A227162 R. H. Hardin, <a href="/A227162/b227162.txt">Table of n, a(n) for n = 1..210</a>
%F A227162 Empirical: a(n) = (1/90720)*n^9 + (1/8064)*n^8 + (17/30240)*n^7 + (13/960)*n^6 - (131/4320)*n^5 + (181/384)*n^4 - (146161/90720)*n^3 + (171511/10080)*n^2 - (25129/504)*n + 58 for n>3.
%F A227162 Conjectures from _Colin Barker_, Sep 07 2018: (Start)
%F A227162 G.f.: x*(4 - 22*x + 62*x^2 - 97*x^3 + 98*x^4 - 56*x^5 + 32*x^6 - 70*x^7 + 123*x^8 - 113*x^9 + 55*x^10 - 13*x^11 + x^12) / (1 - x)^10.
%F A227162 a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>13.
%F A227162 (End)
%e A227162 Some solutions for n=4:
%e A227162 ..1..1..1....1..1..1....1..0..0....1..0..0....1..0..0....0..0..0....0..0..0
%e A227162 ..1..1..0....1..1..1....0..0..1....0..0..1....0..0..0....0..1..1....0..1..1
%e A227162 ..1..1..0....1..1..1....0..0..1....0..0..0....0..0..1....0..1..1....0..1..0
%e A227162 ..1..0..0....1..1..0....0..0..0....0..0..0....0..0..1....0..1..0....0..0..1
%Y A227162 Column 3 of A227165.
%K A227162 nonn
%O A227162 1,1
%A A227162 _R. H. Hardin_, Jul 03 2013