A223919 Number of 2 X n 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

6, 36, 158, 548, 1600, 4102, 9503, 20299, 40570, 76704, 138348, 239630, 400700, 649642, 1024813, 1577669, 2376142, 3508636, 5088714, 7260552, 10205240, 14148014, 19366507, 26200111, 35060546, 46443736, 60943096, 79264338

Offset: 1

Author

R. H. Hardin, Mar 29 2013

Keywords

• nonn

Comments

Row 2 of A223918.

Examples

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

Links

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

Crossrefs

Cf. A223918.

Formula

Empirical: a(n) = (1/10080)*n^8 + (1/504)*n^7 + (1/40)*n^6 + (109/720)*n^5 + (259/480)*n^4 + (173/144)*n^3 + (4877/2520)*n^2 + (481/420)*n + 1.

Conjectures from Colin Barker, Feb 23 2018: (Start)

G.f.: x*(6 - 18*x + 50*x^2 - 82*x^3 + 88*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)