A266937 Number of 4 X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

5, 12, 20, 35, 52, 82, 115, 169, 232, 322, 426, 573, 738, 961, 1215, 1543, 1912, 2382, 2905, 3557, 4280, 5161, 6135, 7308, 8594, 10120, 11791, 13749, 15883, 18361, 21049, 24142, 27490, 31307, 35427, 40093, 45111, 50757, 56818, 63594, 70848, 78917, 87535

Offset: 1

Author

R. H. Hardin, Jan 06 2016

Keywords

• nonn

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..87

Crossrefs

Row 4 of A266935.

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) - a(n-5) - a(n-6) + 2*a(n-8) + 2*a(n-9) - a(n-11) - a(n-12) - a(n-13) - a(n-14) + 2*a(n-15) + a(n-16) -a(n-17).

Empirical g.f.: x*(5 + 7*x - 2*x^2 - 4*x^3 - 6*x^4 - 3*x^5 + x^6 + 9*x^7 + 12*x^8 + 2*x^9 -6*x^10 - 4*x^11 - 6*x^12 - 5*x^13 + 9*x^14 + 6*x^15 - 5*x^16) / ((1 - x)^6*(1 + x)^3*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Jan 10 2019