A186121 - OEIS

A186121

Number of (n+1) X 3 binary arrays with every 2 X 2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2 X 2 subblock diagonal sum less antidiagonal sum.

%I #9 Apr 17 2018 12:12:55

%S 14,38,94,254,682,1878,5214,14606,41138,116350,330046,938174,2670826,

%T 7611430,21707790,61943694,176825074,504902766,1441965358,4118707422,

%U 11765461418,33611411190,96025298558,274346613774,783834214130

%N Number of (n+1) X 3 binary arrays with every 2 X 2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2 X 2 subblock diagonal sum less antidiagonal sum.

%C Column 2 of A186128.

%H R. H. Hardin, <a href="/A186121/b186121.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 5*a(n-1) - 3*a(n-2) - 13*a(n-3) + 6*a(n-4) + 14*a(n-5) + 6*a(n-6) + 8*a(n-7) - 16*a(n-8) - 16*a(n-9).

%F Empirical g.f.: 2*x*(7 - 16*x - 27*x^2 + 40*x^3 + 52*x^4 + 14*x^5 - 4*x^6 - 72*x^7 - 64*x^8) / ((1 - 2*x)*(1 - 3*x - 3*x^2 + 7*x^3 + 8*x^4 + 2*x^5 - 2*x^6 - 12*x^7 - 8*x^8)). - _Colin Barker_, Apr 17 2018

%e Some solutions for 5 X 3:

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

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

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

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

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

%Y Cf. A186128.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 13 2011