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Number of 3X3X3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and every horizontal row having the same average value
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%I #6 Jul 23 2012 13:15:23

%S 2,15,38,79,152,263,418,643,942,1329,1832,2463,3234,4185,5326,6677,

%T 8280,10153,12314,14817,17678,20923,24608,28757,33394,38587,44358,

%U 50739,57800,65571,74082,83415,93598,104669,116712,129763,143858,159093,175502

%N Number of 3X3X3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and every horizontal row having the same average value

%C Row 3 of A214540

%H R. H. Hardin, <a href="/A214541/b214541.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+11*x+8*x^2+3*x^3+4*x^5-x^7-2*x^8+x^9) / ( (1+x)*(1+x+x^2)^2*(x-1)^5 ). - _R. J. Mathar_, Jul 23 2012

%e Some solutions for n=4

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

%e ...2.4....3.1....4.2....3.1....3.3....3.3....1.1....0.0....3.1....2.2....0.2

%e ..4.1.4..3.3.0..4.1.4..2.4.0..3.2.4..3.3.3..1.1.1..0.0.0..3.1.2..1.3.2..0.1.2

%K nonn

%O 1,1

%A _R. H. Hardin_ Jul 20 2012