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A214541 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.

%I A214541 #8 Jul 22 2025 23:17:34
%S A214541 2,15,38,79,152,263,418,643,942,1329,1832,2463,3234,4185,5326,6677,
%T A214541 8280,10153,12314,14817,17678,20923,24608,28757,33394,38587,44358,
%U A214541 50739,57800,65571,74082,83415,93598,104669,116712,129763,143858,159093,175502
%N A214541 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 A214541 Row 3 of A214540
%H A214541 R. H. Hardin, <a href="/A214541/b214541.txt">Table of n, a(n) for n = 1..210</a>
%F A214541 Empirical: a(n) = 2*a(n-1) -3*a(n-4) +3*a(n-6) -2*a(n-9) +a(n-10).
%F A214541 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 A214541 Some solutions for n=4
%e A214541 ....3......2......3......2......3......3......1......0......2......2......1
%e A214541 ...2.4....3.1....4.2....3.1....3.3....3.3....1.1....0.0....3.1....2.2....0.2
%e A214541 ..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 A214541 nonn
%O A214541 1,1
%A A214541 _R. H. Hardin_ Jul 20 2012