A224014 Number of 4 X n 0..2 arrays with rows nondecreasing and antidiagonals unimodal.

81, 1296, 7378, 28541, 90051, 245055, 595822, 1325316, 2742301, 5343468, 9896484, 17548273, 29963249, 49496631, 79408380, 124123708, 189546519, 283432552, 415829406, 599591037, 850974727, 1190328935, 1642880850, 2239632876

Offset

1,1

Comments

Row 4 of A224012.

Links

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

Formula

Empirical: a(n) = (41/4032)*n^8 + (55/336)*n^7 + (733/480)*n^6 + (1037/120)*n^5 + (4789/192)*n^4 + (2125/48)*n^3 + (216821/5040)*n^2 + (9329/210)*n + 4 for n>2.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(81 + 567*x - 1370*x^2 + 1991*x^3 + 132*x^4 - 4590*x^5 + 7855*x^6 - 6900*x^7 + 3514*x^8 - 990*x^9 + 120*x^10) / (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>11.

(End)

Example

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

Crossrefs

Cf. A224012.

Sequence in context: A232876 A224355 A016768 * A059977 A231912 A116205

Adjacent sequences: A224011 A224012 A224013 * A224015 A224016 A224017

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved