A214353 Number of 3 X 3 X 3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

26, 169, 660, 1951, 4822, 10507, 20840, 38421, 66802, 110693, 176188, 271011, 404782, 589303, 838864, 1170569, 1604682, 2164993, 2879204, 3779335, 4902150, 6289603, 7989304, 10055005, 12547106, 15533181, 19088524, 23296715, 28250206

Offset: 1

Author

R. H. Hardin, Jul 13 2012

Keywords

• nonn

Comments

Row 3 of A214352.

Examples

			Some solutions for n=3:
....1......1......2......1......2......1......3......2......3......2......0
...2.0....1.1....2.1....1.1....2.2....1.2....3.1....0.3....0.3....1.3....1.0
..3.2.0..0.3.1..3.1.3..0.3.0..2.2.0..2.1.2..3.1.0..0.3.2..0.1.3..1.2.3..3.1.0
		

Links

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

Crossrefs

Cf. A214352.

Formula

Empirical: a(n) = (1/36)*n^6 + (7/15)*n^5 + (25/9)*n^4 + (15/2)*n^3 + (331/36)*n^2 + (151/30)*n + 1.

Conjectures from Colin Barker, Jul 22 2018: (Start)

G.f.: x*(26 - 13*x + 23*x^2 - 30*x^3 + 20*x^4 - 7*x^5 + x^6) / (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>7.

(End)