A188822 - OEIS

%I #9 Apr 30 2018 09:09:52

%S 128,1156,3888,8836,15776,24964,36000,49284,64416,81796,101024,122500,

%T 145824,171396,198816,228484,260000,293764,329376,367236,406944,

%U 448900,492704,538756,586656,636804,688800,743044,799136,857476,917664,980100

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

%C Column 7 of A188824.

%H R. H. Hardin, <a href="/A188822/b188822.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>7.

%F Conjectures from _Colin Barker_, Apr 30 2018: (Start)

%F 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 a(n) = 2*(578 - 1088*n + 512*n^2) for n>3 and even.

%F a(n) = 2*(528 - 1088*n + 512*n^2) for n>3 and odd.

%F (End)

%e Some solutions for 3 X 7:

%e ..1..1..1..0..1..1..1....1..1..1..1..1..0..1....1..1..1..1..1..1..1

%e ..1..1..0..0..0..0..1....1..1..0..1..0..1..0....1..0..1..0..0..1..0

%e ..0..0..0..0..0..0..0....1..0..1..0..0..0..0....0..1..0..0..0..0..0

%Y Cf. A188824.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 11 2011