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%I #7 Jul 22 2018 08:44:31
%S 2,6,14,29,50,88,136,209,302,430,584,793,1034,1344,1704,2149,2652,
%T 3270,3956,4777,5690,6760,7934,9305,10792,12502,14360,16469,18740,
%U 21312,24062,27145,30444,34110,38010,42337,46916,51960,57302,63149,69314,76054,83134
%N Number of 3 X 3 X 3 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.
%C Row 3 of A214906.
%H R. H. Hardin, <a href="/A214907/b214907.txt">Table of n, a(n) for n = 1..210</a>
%F 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).
%F 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
%e Some solutions for n=4:
%e ....3......2......1......1......1......3......4......2......3......2......2
%e ...3.3....2.2....0.2....1.1....0.2....2.4....4.4....1.3....2.4....0.4....0.4
%e ..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
%Y Cf. A214906.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 29 2012
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