A223927 Number of n X 2 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

9, 54, 218, 698, 1915, 4690, 10511, 21919, 43045, 80334, 143496, 246728, 410255, 662242, 1041133, 1598477, 2402305, 3541126, 5128614, 7309062, 10263683, 14217842, 19449307, 26297611, 35174621, 46576414, 61096564, 79440948

Offset

1,1

Comments

Column 2 of A223933.

Links

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

Formula

Empirical: a(n) = (1/10080)*n^8 + (1/504)*n^7 + (1/40)*n^6 + (109/720)*n^5 + (379/480)*n^4 + (317/144)*n^3 + (8027/2520)*n^2 + (691/420)*n + 1.

Conjectures from Colin Barker, Feb 21 2018: (Start)

G.f.: x*(9 - 27*x + 56*x^2 - 76*x^3 + 79*x^4 - 59*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)

Example

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

Crossrefs

Cf. A223933.

Sequence in context: A034719 A013567 A073974 * A307045 A035927 A250286

Adjacent sequences: A223924 A223925 A223926 * A223928 A223929 A223930

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved