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

Author

R. H. Hardin, Jul 29 2012

Keywords

• nonn

Comments

Row 3 of A214906.

Examples

			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
		

Links

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

Crossrefs

Cf. A214906.

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