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%I #10 Jul 20 2018 09:22:25
%S 0,1,7,28,76,166,316,547,883,1351,1981,2806,3862,5188,6826,8821,11221,
%T 14077,17443,21376,25936,31186,37192,44023,51751,60451,70201,81082,
%U 93178,106576,121366,137641,155497,175033,196351,219556,244756,272062,301588
%N Number of triangular n X n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any neighbor, and containing the value n(n+1)/2-2.
%C Column 1 of A211904.
%H R. H. Hardin, <a href="/A211899/b211899.txt">Table of n, a(n) for n = 1..75</a>
%F Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (13/8)*n^2 + (5/4)*n + 1 for n>1.
%F Conjectures from _Colin Barker_, Jul 20 2018: (Start)
%F G.f.: x^2*(1 + 2*x + 3*x^2 - 4*x^3 + x^4) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
%F (End)
%e Some solutions for n=4:
%e .....0........0........0........0........0........0........0........0
%e ....1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2
%e ...3.4.5....3.4.5....3.4.0....2.3.4....3.4.5....3.4.3....3.4.5....0.3.4
%e ..1.6.7.8..6.7.8.7..5.6.7.8..5.6.7.8..4.6.7.8..5.6.7.8..5.6.7.8..5.6.7.8
%Y Cf. A211904.
%K nonn
%O 1,3
%A _R. H. Hardin_, Apr 25 2012
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