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Number of triangular nXnXn 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)/2-3
0

%I #3 Apr 25 2012 06:54:39

%S 0,1,14,274,2315,11866,44821,137859,365604,866530,1880131,3798191,

%T 7233304,13108109,22769020,38128546,61840611,97513599,149966164,

%U 225531160,332413361,481106956,684879119

%N Number of triangular nXnXn 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)/2-3

%C Column 2 of A211904

%F Empirical: a(n) = (1/128)*n^8 + (1/32)*n^7 - (41/192)*n^6 - (3/8)*n^5 + (329/128)*n^4 - (139/96)*n^3 - (467/96)*n^2 + (127/24)*n for n>1

%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....3.4.5....3.4.5....3.0.4....3.4.5....3.4.0....3.0.1

%e ..4.6.0.7..6.7.6.3..6.7.0.7..4.0.6.7..5.6.7.0..6.7.1.8..5.6.2.7..4.5.6.7

%K nonn

%O 1,3

%A _R. H. Hardin_ Apr 25 2012