A250894 Number of (n+1) X (4+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.

1229, 3867, 12387, 39003, 119359, 357335, 1052787, 3069907, 8903447, 25780959, 74735755, 217269563, 634036815, 1857880039, 5466025571, 16140988131, 47817974983, 142048148015, 422912961915, 1261379418571, 3767513043071

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 23 2018: (Start)

G.f.: x*(1229 - 10881*x + 39723*x^2 - 76719*x^3 + 81484*x^4 - 42988*x^5 + 4192*x^6 + 6688*x^7 - 2560*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).

a(n) = -265 - 21*2^n + 9604*3^(-3+n) + (226-9*2^(3+n))*n + 6*(7+9*2^n)*n^2 for n>2.

(End)

Example

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

Crossrefs

Column 4 of A250898.

Sequence in context: A038824 A038813 A368637 * A251405 A278018 A182721

Adjacent sequences: A250891 A250892 A250893 * A250895 A250896 A250897

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved