A224043 Number of 7 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

128, 987, 2419, 4160, 6321, 9125, 12856, 17875, 24623, 33686, 45837, 62087, 83746, 112495, 150470, 200359, 265513, 350072, 459107, 598779, 776516, 1001209, 1283428, 1635659, 2072563, 2611258, 3271625, 4076639, 5052726, 6230147, 7643410, 9331711

Offset: 1

Author

R. H. Hardin, Mar 30 2013

Keywords

• nonn

Comments

Row 7 of A224038.

Examples

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

Links

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

Crossrefs

Cf. A224038.

Formula

Empirical: a(n) = (1/5040)*n^7 + (17/360)*n^5 + (13/24)*n^4 + (5767/720)*n^3 + (1919/24)*n^2 + (37901/70)*n + 143 for n>5.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(128 - 37*x - 1893*x^2 + 5276*x^3 - 5539*x^4 + 1495*x^5 + 1526*x^6 - 1101*x^7 + 65*x^8 + 155*x^9 - 160*x^10 + 117*x^11 - 31*x^12) / (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>13.

(End)