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 #7 Nov 16 2018 10:57:50
%S 33,85,208,496,1158,2699,6257,14520,33640,77999,180744,419005,971109,
%T 2251135,5217807,12095192,28036004,64988500,150642356,349192782,
%U 809429294,1876272631,4349215350,10081551668,23369149689,54170034264
%N Number of (3+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
%H R. H. Hardin, <a href="/A250732/b250732.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 9*a(n-3) + 12*a(n-4) - 2*a(n-5) - 3*a(n-6) + a(n-7) for n>8.
%F Empirical g.f.: x*(33 - 47*x - 66*x^2 + 131*x^3 - 41*x^4 - 23*x^5 + 14*x^6 - 2*x^7) / ((1 - x)^2*(1 - 2*x - 3*x^2 + 5*x^3 + x^4 - x^5)). - _Colin Barker_, Nov 16 2018
%e Some solutions for n=4:
%e ..0..0..0..0..0....0..0..0..0..1....0..1..0..0..1....0..0..0..0..1
%e ..0..0..0..0..1....0..0..0..1..1....1..0..1..1..1....0..0..1..1..1
%e ..1..0..0..0..1....0..0..0..1..1....0..1..1..1..1....0..1..1..1..1
%e ..0..1..0..1..1....1..1..0..1..1....1..1..1..1..1....1..1..1..1..1
%Y Row 3 of A250729.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 27 2014