A250904 Number of (6+1) X (n+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.

13111, 47061, 136509, 357335, 890199, 2168405, 5232461, 12579759, 30207983, 72567285, 174704109, 422507959, 1029471543, 2535605061, 6334266493, 16097729455, 41712370479, 110334908613, 297924002173, 820272043287

Offset

1,1

Links

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

Formula

Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).

Empirical g.f.: x*(13111 - 136493*x + 592090*x^2 - 1408240*x^3 + 2032769*x^4 - 1861139*x^5 + 1077330*x^6 - 359076*x^7 + 52488*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - Colin Barker, Nov 23 2018

Example

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

Crossrefs

Row 6 of A250898.

Sequence in context: A252548 A015341 A233689 * A250948 A157433 A089212

Adjacent sequences: A250901 A250902 A250903 * A250905 A250906 A250907

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved