A223719 Number of n X 2 0..2 arrays with rows, antidiagonals and columns unimodal.

9, 81, 484, 2116, 7396, 21904, 57121, 134689, 292681, 594441, 1140624, 2085136, 3655744, 6180196, 10118761, 16104169, 24990001, 37908649, 56340036, 82192356, 117896164, 166513216, 231861529, 318658201, 432681601, 580954609, 771950656

Offset

1,1

Comments

Column 2 of A223725.

Links

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

Formula

Empirical: a(n) = (1/576)*n^8 + (1/48)*n^7 + (41/288)*n^6 + (13/24)*n^5 + (793/576)*n^4 + (31/16)*n^3 + (119/48)*n^2 + (3/2)*n + 1.

Conjectures from Colin Barker, Feb 19 2018: (Start)

G.f.: x*(9 + 79*x^2 - 80*x^3 + 106*x^4 - 68*x^5 + 31*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:
..1..0....2..0....1..2....2..0....1..1....2..0....0..2....2..1....1..1....2..2
..1..2....1..2....1..2....0..0....2..2....2..1....2..0....1..1....2..1....1..2
..2..1....1..0....1..2....0..1....0..1....0..0....2..0....1..2....1..1....1..1

Crossrefs

Sequence in context: A207719 A167717 A208079 * A270295 A214618 A343462

Adjacent sequences: A223716 A223717 A223718 * A223720 A223721 A223722

Keyword

nonn

Author

R. H. Hardin, Mar 26 2013

Status

approved