A250779 - OEIS

%I #8 Nov 19 2018 09:14:03

%S 99,238,534,1152,2426,5028,10306,20960,42394,85420,171666,344392,

%T 690122,1381908,2765858,5534192,11071354,22146236,44296626,88598104,

%U 177201834,354410148,708827714,1417663872,2835337306,5670685388,11341382866

%N Number of (n+1) X (4+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

%H R. H. Hardin, <a href="/A250779/b250779.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Nov 19 2018: (Start)

%F G.f.: x*(99 - 356*x + 492*x^2 - 304*x^3 + 73*x^4) / ((1 - x)^4*(1 - 2*x)).

%F a(n) = (-288 + 507*2^n - 116*n - 12*n^2 - 4*n^3) / 6.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 4 of A250783.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014