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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.
1

%I #12 Apr 23 2018 14:22:44

%S 1,1,15,3429,18172005,3030361658604,20538495213667066533,

%T 7069329642959332230532689983,150574890630606350105309341350824904669,

%U 237075065354315062816111131522815337395866137560373,32430625006159571889921247597353572731767630164652210957593666925

%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.

%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 ...2.0.3....3.4.0....2.0.1....0.3.4....3.4.0....3.4.0....3.4.5....3.4.0

%e ..3.1.4.1..4.2.5.4..3.1.3.0..4.5.2.5..0.5.3.6..4.5.3.6..5.0.2.1..1.2.3.5

%Y Cf. A182797, A193283.

%K nonn

%O 1,3

%A _R. H. Hardin_, Apr 23 2012

%E a(7)-a(11) from _Andrew Howroyd_, Apr 23 2018