A204649 Number of (n+1) X 7 0..1 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.

132, 200, 434, 938, 1918, 3702, 6780, 11868, 19969, 32450, 51134, 78404, 117324, 171774, 246604, 347804, 482695, 660138, 890766, 1187236, 1564506, 2040134, 2634604, 3371676, 4278765, 5387346, 6733390, 8357828, 10307048, 12633422

Offset

1,1

Comments

Column 6 of A204651.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -20*a(n-2) +28*a(n-3) -14*a(n-4) -14*a(n-5) +28*a(n-6) -20*a(n-7) +7*a(n-8) -a(n-9) for n>13.

Empirical g.f.: x*(132 - 724*x + 1674*x^2 - 1796*x^3 + 280*x^4 + 1532*x^5 - 1858*x^6 + 992*x^7 - 255*x^8 + 15*x^9 + 26*x^10 - 22*x^11 + 6*x^12) / ((1 - x)^8*(1 + x)). - Colin Barker, Jun 08 2018

Example

Some solutions for n=5:
..0..0..0..1..1..1..1....0..0..0..0..0..0..1....0..0..0..0..0..0..0
..0..0..1..1..1..1..1....0..0..0..0..0..0..1....0..0..0..0..0..1..1
..0..0..1..1..1..1..1....0..0..0..0..0..0..1....0..0..1..1..1..1..1
..0..0..1..1..1..1..1....0..0..0..0..1..1..1....0..0..1..1..1..1..1
..0..0..1..1..1..1..1....0..0..0..1..1..1..1....0..1..1..1..1..1..1
..0..1..1..1..1..1..1....1..1..1..1..1..1..1....1..1..1..1..1..1..1

Crossrefs

Cf. A204651.

Sequence in context: A030026 A102474 A015235 * A224548 A253510 A253503

Adjacent sequences: A204646 A204647 A204648 * A204650 A204651 A204652

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved