A223840 Number of 4 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

5, 25, 89, 249, 596, 1286, 2578, 4886, 8851, 15439, 26072, 42800, 68523, 107273, 164567, 247843, 366992, 535000, 768715, 1089755, 1525574, 2110704, 2888192, 3911252, 5245153, 6969365, 9179986, 11992474, 15544709, 20000411, 25552941, 32429513, 40895846, 51261286

Offset: 1

Author

R. H. Hardin, Mar 27 2013

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 4 of A223838.

Formula

Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 + (19/2880)*n^6 + (7/180)*n^5 + (527/5760)*n^4 + (3683/1440)*n^3 + (4051/10080)*n^2 - (1707/280)*n + 13 for n>2.

Conjectures from Colin Barker, Aug 24 2018: (Start)

G.f.: x*(5 - 20*x + 44*x^2 - 72*x^3 + 89*x^4 - 70*x^5 + 28*x^6 - 4*x^7 + 4*x^8 - 4*x^9 + x^10) / (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>11.

(End)

Extensions

Name corrected by Andrew Howroyd, Mar 20 2025