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

1,1

Comments

Row 3 of A214352.

Links

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

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)

Example

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

Crossrefs

Cf. A214352.

Sequence in context: A006354 A249292 A279744 * A283567 A037052 A156339

Adjacent sequences: A214350 A214351 A214352 * A214354 A214355 A214356

Keyword

nonn

Author

R. H. Hardin, Jul 13 2012

Status

approved