A250897 Number of (n+1) X (7+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.

32095, 88421, 244200, 680504, 1893433, 5232461, 14283986, 38498188, 102731213, 272597111, 722672320, 1922589386, 5152218779, 13948044421, 38216305022, 106061750888, 298128374761, 848068491251, 2438292434012, 7074745440934

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..196

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*(32095 - 296719*x + 1108848*x^2 - 2144026*x^3 + 2239408*x^4 - 1181770*x^5+ 162292*x^6 + 174146*x^7 - 73990*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).

a(n) = -17515/4 + 4833*2^(-1+n) + (198025*3^(-3+n))/4 + (23737/2-28323*2^(-5+n))*n + (5071+53217*2^(-5+n))*n^2 for n>2.

(End)

Example

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

Crossrefs

Column 7 of A250898.

Sequence in context: A097282 A264499 A249230 * A366512 A146896 A205930

Adjacent sequences: A250894 A250895 A250896 * A250898 A250899 A250900

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved