A225009 Number of n X 7 0..1 arrays with rows unimodal and columns nondecreasing.

29, 239, 1163, 4166, 12174, 30738, 69498, 144111, 278707, 508937, 885677, 1479452, 2385644, 3730548, 5678340, 8439021, 12277401, 17523187, 24582239, 33949058, 46220570, 62111270, 82469790, 108296955, 140765391, 181240749, 231304609

Offset: 1

Author

R. H. Hardin, Apr 23 2013

Keywords

• nonn

Examples

			Some solutions for n=3:
..0..1..1..0..0..0..0....1..1..1..1..0..0..0....0..0..0..0..0..0..0
..0..1..1..1..1..0..0....1..1..1..1..1..0..0....1..1..0..0..0..0..0
..1..1..1..1..1..1..1....1..1..1..1..1..1..1....1..1..0..0..0..0..0
		

Links

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

Crossrefs

Column 7 of A225010.

Formula

Empirical: a(n) = (4/315)*n^7 + (1/5)*n^6 + (58/45)*n^5 + (35/8)*n^4 + (1507/180)*n^3 + (357/40)*n^2 + (2027/420)*n + 1.

Conjectures from Colin Barker, Sep 05 2018: (Start)

G.f.: x*(29 + 7*x + 63*x^2 - 70*x^3 + 56*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)