A224159 Number of 3 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

8, 36, 89, 187, 373, 702, 1252, 2130, 3479, 5486, 8391, 12497, 18181, 25906, 36234, 49840, 67527, 90242, 119093, 155367, 200549, 256342, 324688, 407790, 508135, 628518, 772067, 942269, 1142997, 1378538, 1653622, 1973452, 2343735, 2770714

Offset: 1

Author

R. H. Hardin, Mar 31 2013

Keywords

• nonn

Comments

Row 3 of A224158.

Examples

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

Links

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

Crossrefs

Cf. A224158.

Formula

Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (47/144)*n^4 - (3/16)*n^3 + (1111/180)*n^2 - (199/60)*n + 20 for n>2.

Conjectures from Colin Barker, Aug 28 2018: (Start)

G.f.: x*(8 - 20*x + 5*x^2 + 40*x^3 - 47*x^4 - 5*x^5 + 41*x^6 - 27*x^7 + 6*x^8) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.

(End)