A224014 Number of 4 X n 0..2 arrays with rows nondecreasing and antidiagonals unimodal.

81, 1296, 7378, 28541, 90051, 245055, 595822, 1325316, 2742301, 5343468, 9896484, 17548273, 29963249, 49496631, 79408380, 124123708, 189546519, 283432552, 415829406, 599591037, 850974727, 1190328935, 1642880850, 2239632876

Offset: 1

Author

R. H. Hardin, Mar 30 2013

Keywords

• nonn

Comments

Row 4 of A224012.

Examples

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

Links

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

Crossrefs

Cf. A224012.

Formula

Empirical: a(n) = (41/4032)*n^8 + (55/336)*n^7 + (733/480)*n^6 + (1037/120)*n^5 + (4789/192)*n^4 + (2125/48)*n^3 + (216821/5040)*n^2 + (9329/210)*n + 4 for n>2.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(81 + 567*x - 1370*x^2 + 1991*x^3 + 132*x^4 - 4590*x^5 + 7855*x^6 - 6900*x^7 + 3514*x^8 - 990*x^9 + 120*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)