A250779 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.

99, 238, 534, 1152, 2426, 5028, 10306, 20960, 42394, 85420, 171666, 344392, 690122, 1381908, 2765858, 5534192, 11071354, 22146236, 44296626, 88598104, 177201834, 354410148, 708827714, 1417663872, 2835337306, 5670685388, 11341382866

Offset

1,1

Links

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

Formula

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

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

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

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

(End)

Example

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

Crossrefs

Column 4 of A250783.

Sequence in context: A260242 A250734 A260279 * A259995 A125820 A008902

Adjacent sequences: A250776 A250777 A250778 * A250780 A250781 A250782

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved