A250780 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.

209, 518, 1194, 2640, 5688, 12036, 25126, 51904, 106344, 216500, 438614, 885336, 1782168, 3580356, 7182678, 14395024, 28829560, 57711060, 115489574, 231065768, 462241608, 924621732, 1849416198, 3699045984, 7398353992, 14797027060

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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).

Conjectures from Colin Barker, Nov 19 2018: (Start)

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)).

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

(End)

Example

Some solutions for n=4:
..1..0..0..0..1..0....0..0..1..0..0..0....1..0..0..0..0..0....0..1..0..0..0..0
..1..0..0..1..0..1....0..0..1..0..0..0....1..0..0..0..0..1....0..1..0..0..0..1
..1..0..1..0..1..0....0..0..1..0..0..0....1..0..0..0..0..1....0..1..0..0..1..0
..1..0..1..1..0..1....0..0..1..0..0..0....1..0..0..0..0..1....0..1..0..0..1..0
..1..0..1..1..0..1....0..0..1..0..0..1....1..1..1..1..1..0....1..0..1..1..0..1

Crossrefs

Column 5 of A250783.

Sequence in context: A304154 A305507 A211672 * A305173 A316761 A260011

Adjacent sequences: A250777 A250778 A250779 * A250781 A250782 A250783

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved