A224411 Number of 4 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

16, 108, 358, 884, 1928, 3902, 7490, 13784, 24467, 42053, 70195, 114073, 180875, 280385, 425693, 634043, 927836, 1335806, 1894388, 2649298, 3657346, 4988504, 6728252, 8980226, 11869193, 15544379, 20183177, 25995263, 33227149, 42167203

Offset: 1

Author

R. H. Hardin, Apr 05 2013

Keywords

• nonn

Comments

Row 4 of A224409.

Examples

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

Links

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

Crossrefs

Cf. A224409.

Formula

Empirical: a(n) = (1/40320)*n^8 + (1/1440)*n^7 + (31/2880)*n^6 + (13/144)*n^5 + (3767/5760)*n^4 + (6409/1440)*n^3 + (189859/10080)*n^2 - (73/24)*n - 7 for n>2.

Conjectures from Colin Barker, Aug 30 2018: (Start)

G.f.: x*(16 - 36*x - 38*x^2 + 206*x^3 - 196*x^4 - 106*x^5 + 368*x^6 - 334*x^7 + 155*x^8 - 38*x^9 + 4*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)