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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 (list; graph; refs; listen; history; text; internal format)
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: A027083 A249665 A321027 * A169948 A192705 A123991

Adjacent sequences:  A214904 A214905 A214906 * A214908 A214909 A214910

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 29 2012

STATUS

approved

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Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)