A223682 Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal.

16, 256, 2032, 9822, 35509, 105995, 275775, 646407, 1395174, 2815594, 5372794, 9777124, 17079747, 28794301, 47049089, 74774613, 115931628, 175785252, 261231028, 381179194, 547003777, 773063487, 1077301747, 1481933555

Offset: 1

Author

R. H. Hardin, Mar 25 2013

Keywords

• nonn

Comments

Row 4 of A223680.

Examples

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

Links

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

Crossrefs

Cf. A223680.

Formula

Empirical: a(n) = (1/112)*n^8 + (79/1260)*n^7 + (121/120)*n^6 + (71/36)*n^5 + (475/48)*n^4 - (1757/180)*n^3 + (8893/840)*n^2 - (569/84)*n + 9.

Conjectures from Colin Barker, Aug 22 2018: (Start)

G.f.: x*(16 + 112*x + 304*x^2 - 594*x^3 + 775*x^4 - 442*x^5 + 216*x^6 - 36*x^7 + 9*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)