A250733 Number of (4+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

58, 144, 365, 885, 2092, 4889, 11377, 26419, 61330, 142336, 330417, 767047, 1781019, 4135537, 9603827, 22303104, 51797791, 120298572, 279397140, 648909915, 1507137312, 3500429630, 8130041844, 18882699707, 43856786967, 101861340070

Offset: 1

Author

R. H. Hardin, Nov 27 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 4 of A250729.

Formula

Empirical: a(n) = 4*a(n-1) - a(n-2) - 13*a(n-3) + 15*a(n-4) + 3*a(n-5) - 11*a(n-6) + 4*a(n-7) for n>9.

Empirical g.f.: x*(58 - 88*x - 153*x^2 + 323*x^3 - 81*x^4 - 183*x^5 + 149*x^6 - 22*x^7 - 8*x^8) / ((1 - x)^2*(1 - 2*x - 4*x^2 + 7*x^3 + 3*x^4 - 4*x^5)). - Colin Barker, Nov 16 2018