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

Author

R. H. Hardin, Apr 04 2013

Keywords

• nonn

Comments

Row 3 of A224353.

Examples

			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
		

Links

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

Crossrefs

Cf. A224353.

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)