A224354 Number of 3 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

27, 216, 788, 2321, 5840, 13052, 26610, 50423, 90012, 152912, 249120, 391589, 596768, 885188, 1282094, 1818123, 2530028, 3461448, 4663724, 6196761, 8129936, 10543052, 13527338, 17186495, 21637788, 27013184, 33460536, 41144813, 50249376

Offset

1,1

Comments

Row 3 of A224353.

Links

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

Formula

Empirical: a(n) = (23/360)*n^6 + (19/40)*n^5 + (235/72)*n^4 + (61/8)*n^3 + (1921/180)*n^2 + (189/10)*n + 3 for n>1.

Conjectures from Colin Barker, Aug 29 2018: (Start)

G.f.: x*(27 + 27*x - 157*x^2 + 396*x^3 - 474*x^4 + 326*x^5 - 116*x^6 + 17*x^7) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>8.

(End)

Example

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

Crossrefs

Cf. A224353.

Sequence in context: A224874 A125111 A016767 * A224013 A059827 A117688

Adjacent sequences: A224351 A224352 A224353 * A224355 A224356 A224357

Keyword

nonn

Author

R. H. Hardin, Apr 04 2013

Status

approved