A224186 Number of n X 4 0..2 arrays with rows unimodal and columns nondecreasing.

46, 548, 3526, 15779, 55438, 163746, 424326, 992607, 2138488, 4305730, 8191976, 14853709, 25840868, 43366252, 70515252, 111501861, 171977322, 259398184, 383460946, 556610879, 794633026, 1117333790, 1549321930, 2120898195

Offset: 1

Author

R. H. Hardin, Apr 01 2013

Keywords

• nonn

Comments

Column 4 of A224190.

Examples

			Some solutions for n=3:
..0..1..0..0....1..1..1..1....2..1..0..0....0..1..2..0....0..1..0..0
..1..1..0..0....1..1..1..1....2..1..1..0....0..2..2..0....0..1..1..0
..1..2..0..0....1..1..1..1....2..2..1..1....0..2..2..0....1..1..1..0
		

Links

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

Crossrefs

Cf. A224190.

Formula

Empirical: a(n) = (41/4032)*n^8 + (55/336)*n^7 + (179/160)*n^6 + (169/40)*n^5 + (615/64)*n^4 + (215/16)*n^3 + (56759/5040)*n^2 + (2173/420)*n + 1.

Conjectures from Colin Barker, Aug 29 2018: (Start)

G.f.: x*(46 + 134*x + 250*x^2 - 91*x^3 + 127*x^4 - 84*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)