A214907 Number of 3 X 3 X 3 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

2, 6, 14, 29, 50, 88, 136, 209, 302, 430, 584, 793, 1034, 1344, 1704, 2149, 2652, 3270, 3956, 4777, 5690, 6760, 7934, 9305, 10792, 12502, 14360, 16469, 18740, 21312, 24062, 27145, 30444, 34110, 38010, 42337, 46916, 51960, 57302, 63149, 69314, 76054, 83134

Offset

1,1

Comments

Row 3 of A214906.

Links

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

Formula

Empirical: a(n) = 2*a(n-2) + 2*a(n-3) - 4*a(n-5) - 3*a(n-6) + 3*a(n-8) + 4*a(n-9) - 2*a(n-11) - 2*a(n-12) + a(n-14).

G.f.: x*(2 + 6*x + 10*x^2 + 13*x^3 + 10*x^4 + 10*x^5 + 8*x^6 + 7*x^7 + 6*x^8 + x^9 - 2*x^10 - 2*x^11 + x^13) / ((1 - x)^5*(1 + x)^3*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, Jul 22 2018

Example

Some solutions for n=4:
....3......2......1......1......1......3......4......2......3......2......2
...3.3....2.2....0.2....1.1....0.2....2.4....4.4....1.3....2.4....0.4....0.4
..1.4.4..1.2.3..0.1.2..0.1.2..0.0.3..2.3.4..4.4.4..1.2.3..3.3.3..1.1.4..0.3.3

Crossrefs

Cf. A214906.

Sequence in context: A249665 A337106 A321027 * A169948 A192705 A123991

Adjacent sequences: A214904 A214905 A214906 * A214908 A214909 A214910

Keyword

nonn

Author

R. H. Hardin, Jul 29 2012

Status

approved