A215183 Number of 3 X 3 X 3 triangular 0..n arrays with every horizontal row nondecreasing, first elements of rows nonincreasing, last elements of rows nondecreasing, and every row having the same average value.

2, 5, 12, 22, 38, 64, 98, 145, 210, 291, 394, 526, 684, 876, 1110, 1383, 1704, 2083, 2516, 3014, 3588, 4234, 4964, 5791, 6710, 7735, 8880, 10140, 11530, 13066, 14742, 16575, 18582, 20757, 23118, 25684, 28448, 31430, 34650, 38101, 41804, 45781, 50024, 54556

Offset

1,1

Comments

Row 3 of A215182.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - 3*a(n-4) + 3*a(n-6) - 2*a(n-9) + a(n-10).

Empirical g.f.: x*(2 + x + 2*x^2 - 2*x^3 + 3*x^5 - 2*x^8 + x^9) / ((1 - x)^5*(1 + x)*(1 + x + x^2)^2). - Colin Barker, Jul 22 2018

Example

Some solutions for n=4:
....1......3......2......2......1......1......3......0......2......3......4
...1.1....3.3....1.3....2.2....0.2....0.2....3.3....0.0....1.3....3.3....4.4
..1.1.1..3.3.3..0.3.3..2.2.2..0.1.2..0.0.3..1.4.4..0.0.0..1.1.4..2.3.4..4.4.4

Crossrefs

Cf. A215182.

Sequence in context: A048840 A116718 A026035 * A086734 A123647 A166249

Adjacent sequences: A215180 A215181 A215182 * A215184 A215185 A215186

Keyword

nonn

Author

R. H. Hardin, Aug 05 2012

Status

approved