A250780 - OEIS

%I #8 Nov 19 2018 09:14:08

%S 209,518,1194,2640,5688,12036,25126,51904,106344,216500,438614,885336,

%T 1782168,3580356,7182678,14395024,28829560,57711060,115489574,

%U 231065768,462241608,924621732,1849416198,3699045984,7398353992,14797027060

%N Number of (n+1) X (5+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="/A250780/b250780.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 27*a(n-2) + 50*a(n-3) - 55*a(n-4) + 36*a(n-5) - 13*a(n-6) + 2*a(n-7).

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

%F G.f.: x*(209 - 1154*x + 2693*x^2 - 3376*x^3 + 2401*x^4 - 922*x^5 + 153*x^6) / ((1 - x)^6*(1 - 2*x)).

%F a(n) = (9/2)*(49*2^n-32) - (374*n)/5 - 9*n^2 - (25*n^3)/6 - n^5/30.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 5 of A250783.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014