Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Jun 14 2018 16:22:25
%S 16,24,34,50,72,105,154,229,345,527,815,1274,2009,3190,5092,8160,
%T 13114,21119,34060,54987,88835,143589,232169,375480,607347,982500,
%U 1589494,2571614,4160700,6731877,10892110,17623489,28515069,46137995,74652467
%N Number of (n+1) X 2 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
%C Column 1 of A206267.
%H R. H. Hardin, <a href="/A206260/b206260.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n>6.
%F Empirical g.f.: x*(16 - 40*x + 18*x^2 + 18*x^3 - 14*x^4 + x^5) / ((1 - x)^3*(1 - x - x^2)). - _Colin Barker_, Jun 14 2018
%e Some solutions for n=4:
%e ..0..0....0..1....0..1....1..1....1..0....1..1....0..0....1..1....0..0....1..0
%e ..0..1....1..0....1..0....0..0....0..0....1..1....1..0....1..0....0..0....1..1
%e ..1..0....0..1....0..1....0..0....0..0....1..1....1..1....0..0....0..0....0..1
%e ..0..1....1..0....0..1....0..0....0..0....1..0....0..1....0..0....0..0....0..0
%e ..1..0....0..1....1..0....0..0....0..0....1..0....0..0....0..0....0..0....1..0
%Y Cf. A206267.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2012