A224148 Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

5, 25, 92, 272, 691, 1573, 3296, 6472, 12058, 21506, 36961, 61517, 99542, 157084, 242371, 366419, 543763, 793327, 1139450, 1613086, 2253197, 3108359, 4238602, 5717506, 7634576, 10097920, 13237255, 17207267, 22191352, 28405766, 36104213

Offset: 1

Author

R. H. Hardin, Mar 31 2013

Keywords

• nonn

Comments

Row 4 of A224146.

Examples

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

Links

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

Crossrefs

Cf. A224146.

Formula

Empirical: a(n) = (1/40320)*n^8 + (1/3360)*n^7 + (1/192)*n^6 + (1/16)*n^5 + (223/640)*n^4 + (149/160)*n^3 + (3319/2016)*n^2 + (169/168)*n + 1.

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

G.f.: x*(5 - 20*x + 47*x^2 - 76*x^3 + 85*x^4 - 62*x^5 + 29*x^6 - 8*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)