cp's OEIS Frontend

A188822 Number of n X 7 binary arrays without the pattern 0 1 diagonally or antidiagonally.

%I A188822 #9 Apr 30 2018 09:09:52
%S A188822 128,1156,3888,8836,15776,24964,36000,49284,64416,81796,101024,122500,
%T A188822 145824,171396,198816,228484,260000,293764,329376,367236,406944,
%U A188822 448900,492704,538756,586656,636804,688800,743044,799136,857476,917664,980100
%N A188822 Number of n X 7 binary arrays without the pattern 0 1 diagonally or antidiagonally.
%C A188822 Column 7 of A188824.
%H A188822 R. H. Hardin, <a href="/A188822/b188822.txt">Table of n, a(n) for n = 1..200</a>
%F A188822 Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>7.
%F A188822 Conjectures from _Colin Barker_, Apr 30 2018: (Start)
%F A188822 G.f.: 4*x*(32 + 225*x + 394*x^2 + 329*x^3 + 72*x^4 + 8*x^5 - 36*x^6) / ((1 - x)^3*(1 + x)).
%F A188822 a(n) = 2*(578 - 1088*n + 512*n^2) for n>3 and even.
%F A188822 a(n) = 2*(528 - 1088*n + 512*n^2) for n>3 and odd.
%F A188822 (End)
%e A188822 Some solutions for 3 X 7:
%e A188822 ..1..1..1..0..1..1..1....1..1..1..1..1..0..1....1..1..1..1..1..1..1
%e A188822 ..1..1..0..0..0..0..1....1..1..0..1..0..1..0....1..0..1..0..0..1..0
%e A188822 ..0..0..0..0..0..0..0....1..0..1..0..0..0..0....0..1..0..0..0..0..0
%Y A188822 Cf. A188824.
%K A188822 nonn
%O A188822 1,1
%A A188822 _R. H. Hardin_, Apr 11 2011