A250905 Number of (7+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.

40357, 144442, 412006, 1052787, 2553537, 6060594, 14283986, 33622407, 79146865, 186303082, 438524102, 1032952851, 2438864985, 5785894874, 13834474066, 33456261815, 82124660857, 205298412354, 524006897206, 1367662361011

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..128

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*(40357 - 420556*x + 1820163*x^2 - 4302685*x^3 + 6157204*x^4 - 5596797*x^5 + 3233842*x^6 - 1077420*x^7 + 157464*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - Colin Barker, Nov 23 2018

Example

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

Crossrefs

Row 7 of A250898.

Sequence in context: A172632 A255358 A229675 * A250949 A276567 A216291

Adjacent sequences: A250902 A250903 A250904 * A250906 A250907 A250908

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved