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%I #6 Apr 26 2021 19:15:28
%S 2,9,26,83,192,445,892,1752,3136,5494,9074,14716,22842,34868,51570,
%T 75217,106968,150289,207026,282233,378516,503027,659558,857984,
%U 1103346,1408886,1781610,2238970,2789894,3457002,4252128,5204053,6327530,7658725,9216516
%N Number of 4 X 4 X 4 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 4 of A215182.
%H R. H. Hardin, <a href="/A215184/b215184.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) -2*a(n-2) +3*a(n-3) -2*a(n-4) +2*a(n-6) -6*a(n-7) +9*a(n-8) -12*a(n-9) +10*a(n-10) -7*a(n-11) +3*a(n-12) +6*a(n-13) -12*a(n-14) +19*a(n-15) -21*a(n-16) +20*a(n-17) -14*a(n-18) +3*a(n-19) +3*a(n-20) -14*a(n-21) +20*a(n-22) -21*a(n-23) +19*a(n-24) -12*a(n-25) +6*a(n-26) +3*a(n-27) -7*a(n-28) +10*a(n-29) -12*a(n-30) +9*a(n-31) -6*a(n-32) +2*a(n-33) -2*a(n-35) +3*a(n-36) -2*a(n-37) +2*a(n-38) -a(n-39).
%e Some solutions for n=4
%e .....1........2........1........1........2........1........1........1
%e ....1.1......1.3......0.2......1.1......1.3......1.1......0.2......1.1
%e ...1.1.1....1.1.4....0.0.3....0.0.3....0.2.4....1.1.1....0.1.2....0.1.2
%e ..1.1.1.1..0.2.2.4..0.0.1.3..0.0.1.3..0.0.4.4..0.1.1.2..0.0.2.2..0.0.2.2
%Y Cf. A215182.
%K nonn
%O 1,1
%A _R. H. Hardin_ Aug 05 2012
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