A250891 Number of (n+1) X (1+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.

37, 125, 413, 1333, 4213, 13111, 40357, 123271, 374509, 1133503, 3421621, 10309399, 31021885, 93262255, 280198405, 841455367, 2526160141, 7582215967, 22754413909, 68279363575, 204871514077, 614683748239, 1844194375333, 5532878824423

Offset

1,1

Comments

Column 1 of A250898.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 23*a(n-2) + 28*a(n-3) - 12*a(n-4) for n > 6.

Empirical g.f.: x*(37 - 171*x + 264*x^2 - 132*x^3 - 8*x^4 + 2*x^5) / ((1 - x)*(1 - 2*x)^2*(1 - 3*x)). - Colin Barker, Mar 19 2018

Example

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

Crossrefs

Cf. A250898.

Sequence in context: A044288 A044669 A048510 * A250898 A165811 A142331

Adjacent sequences: A250888 A250889 A250890 * A250892 A250893 A250894

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved