%I #8 Jul 22 2018 12:32:05

%S 2,5,12,22,38,64,98,145,210,291,394,526,684,876,1110,1383,1704,2083,

%T 2516,3014,3588,4234,4964,5791,6710,7735,8880,10140,11530,13066,14742,

%U 16575,18582,20757,23118,25684,28448,31430,34650,38101,41804,45781,50024,54556

%N 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.

%C Row 3 of A215182.

%H R. H. Hardin, <a href="/A215183/b215183.txt">Table of n, a(n) for n = 1..210</a>

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

%F 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

%e Some solutions for n=4:

%e ....1......3......2......2......1......1......3......0......2......3......4

%e ...1.1....3.3....1.3....2.2....0.2....0.2....3.3....0.0....1.3....3.3....4.4

%e ..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

%Y Cf. A215182.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 05 2012