A203721 Number of (n+1) X 2 0..2 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.

32, 113, 326, 888, 2278, 5653, 13665, 32440, 75965, 176104, 405154, 926794, 2110867, 4791921, 10851104, 24525361, 55351946, 124789380, 281102434, 632821501, 1423947009, 3202968748, 7202709761, 16193929296, 36403520114, 81824939598

Offset

1,1

Comments

Column 1 of A203728.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -11*a(n-2) +a(n-3) +16*a(n-4) -10*a(n-5) -7*a(n-6) +6*a(n-7) +a(n-8) -a(n-9).

Empirical g.f.: x*(32 - 79*x + 143*x^3 - 89*x^4 - 61*x^5 + 55*x^6 + 6*x^7 - 9*x^8) / ((1 - x)^2*(1 - x - x^2)^2*(1 - 2*x - x^2 + x^3)). - Colin Barker, Jun 04 2018

Example

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

Crossrefs

Cf. A203728.

Sequence in context: A044283 A044664 A221685 * A231527 A298201 A234443

Adjacent sequences: A203718 A203719 A203720 * A203722 A203723 A203724

Keyword

nonn

Author

R. H. Hardin, Jan 05 2012

Status

approved