A250896 Number of (n+1) X (6+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.

10875, 31215, 91030, 265546, 764315, 2168405, 6060594, 16732140, 45832201, 125162059, 342287192, 940831202, 2606118783, 7287014385, 20581424254, 58711891192, 169046356181, 490755132023, 1434774937860, 4219275237870

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*(10875 - 99285*x + 368950*x^2 - 715664*x^3 + 755858*x^4 - 402400*x^5 + 50022*x^6 + 63432*x^7 - 26568*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).

a(n) = (-8787 + 3389*2^n + 169*3^(3+n) + (14186-99*2^(4+n))*n + 36*(145+33*2^(1+n))*n^2) / 4 for n>2.

(End)

Example

Some solutions for n=3:
..2..1..1..0..0..1..0....0..1..1..1..0..0..0....0..1..0..1..0..0..0
..1..2..2..1..1..2..1....0..1..1..1..0..0..0....0..1..0..1..0..0..0
..0..1..1..0..0..1..0....0..1..1..1..1..1..1....0..1..0..1..0..0..0
..0..1..1..0..0..2..1....0..1..1..1..1..2..2....0..1..0..2..2..2..2

Crossrefs

Column 6 of A250898.

Sequence in context: A250954 A334003 A214243 * A164824 A329196 A083513

Adjacent sequences: A250893 A250894 A250895 * A250897 A250898 A250899

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved