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A214907
Number of 3 X 3 X 3 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jul 29 2012
STATUS
approved