A250892 Number of (n+1) X (2+1) 0..2 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.

127, 431, 1450, 4750, 15111, 47061, 144442, 439056, 1326285, 3990883, 11981256, 35923998, 107646283, 322490625, 966132822, 2894737036, 8674725225, 26000484927, 77943849220, 233694315930, 700761297831, 2101539929629

Offset

1,1

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 60*a(n-2) + 162*a(n-3) - 255*a(n-4) + 234*a(n-5) - 116*a(n-6) + 24*a(n-7) for n>9.

Conjectures from Colin Barker, Nov 22 2018: (Start)

G.f.: x*(127 - 1093*x + 3898*x^2 - 7364*x^3 + 7674*x^4 - 3984*x^5 + 498*x^6 + 328*x^7 - 88*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).

a(n) = (567 - 3807*2^n + 7225*3^n - 54*(-1+15*2^n)*n + 54*(-2+3*2^n)*n^2) / 108 for n>2.

(End)

Example

Some solutions for n=4:
..1..1..0....2..0..0....2..1..0....1..0..0....1..0..0....2..2..0....1..1..1
..1..1..1....2..0..0....2..1..2....2..2..2....1..1..1....1..1..1....2..2..2
..1..1..1....1..1..1....2..1..2....2..2..2....0..0..0....0..0..0....0..0..0
..1..2..2....2..2..2....1..0..1....2..2..2....0..0..2....0..1..1....0..2..2
..0..1..1....2..2..2....0..1..2....1..1..1....0..0..2....0..1..2....0..2..2

Crossrefs

Column 2 of A250898.

Sequence in context: A142384 A298237 A299363 * A129537 A057814 A038646

Adjacent sequences: A250889 A250890 A250891 * A250893 A250894 A250895

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved