A223982 Number of n X 3 0..3 arrays with rows unimodal and columns nondecreasing.

50, 684, 5029, 25410, 99634, 325120, 922768, 2346883, 5462600, 11818092, 24045385, 46430852, 85704412, 152105120, 260790200, 433664645, 701719286, 1107976716, 1711156645, 2590185158, 3849685950, 5626605920, 8098142520, 11491155975

Offset: 1

Author

R. H. Hardin, Mar 30 2013

Keywords

• nonn

Comments

Column 3 of A223987.

Examples

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

Links

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

Crossrefs

Cf. A223987.

Formula

Empirical: a(n) = (353/181440)*n^9 + (5/126)*n^8 + (10571/30240)*n^7 + (251/144)*n^6 + (46793/8640)*n^5 + (1565/144)*n^4 + (159679/11340)*n^3 + (715/63)*n^2 + (6491/1260)*n + 1.

Conjectures from Colin Barker, Aug 25 2018: (Start)

G.f.: x*(50 + 184*x + 439*x^2 - 100*x^3 + 259*x^4 - 210*x^5 + 120*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)