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

1,1

Comments

Column 3 of A223987.

Links

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

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)

Example

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

Crossrefs

Cf. A223987.

Sequence in context: A052460 A224168 A223859 * A128799 A231835 A206120

Adjacent sequences: A223979 A223980 A223981 * A223983 A223984 A223985

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved