A250732 - 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