A224040 Number of 4 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

16, 55, 105, 168, 252, 363, 508, 695, 933, 1232, 1603, 2058, 2610, 3273, 4062, 4993, 6083, 7350, 8813, 10492, 12408, 14583, 17040, 19803, 22897, 26348, 30183, 34430, 39118, 44277, 49938, 56133, 62895, 70258, 78257, 86928, 96308, 106435, 117348

Offset: 1

Author

R. H. Hardin, Mar 30 2013

Keywords

• nonn

Comments

Row 4 of A224038.

Examples

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

Links

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

Crossrefs

Cf. A224038.

Formula

Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (83/24)*n^2 + (89/4)*n - 3 for n>2.

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

G.f.: x*(16 - 25*x - 10*x^2 + 33*x^3 - 8*x^4 - 8*x^5 + 3*x^6) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.

(End)