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%I #8 Sep 20 2023 18:49:11
%S 1,1,1,1,7,1,1,10,138,1,1,10,306,8353,1,1,10,342,34489,1563486,1,1,10,
%T 351,44530,14162520,896267399,1,1,10,351,47356,22155653,21101953059,
%U 1563576619949,1,1,10,351,47518,24754099,42007776880,113688398105827
%N T(n,k) is the number of triangular n X n X n arrays of occupancy after each element either stays or moves to some neighbor and with no occupancy greater than k.
%e Table starts:
%e .1.............1...............1...........1........1.....1...1..1.1
%e .1.............7..............10..........10.......10....10..10.10
%e .1...........138.............306.........342......351...351.351
%e .1..........8353...........34489.......44530....47356.47518
%e .1.......1563486........14162520....22155653.24754099
%e .1.....896267399.....21101953059.42007776880
%e .1.1563576619949.113688398105827
%e ...
%e Some solutions for n=4 and k=4:
%e .....0........2........3........0........0........0........2........2
%e ....1.1......1.1......0.0......0.3......2.0......1.1......0.0......0.0
%e ...1.0.2....2.1.0....1.1.2....3.2.0....0.0.1....2.1.3....0.0.1....0.4.0
%e ..2.0.0.3..1.0.0.2..3.0.0.0..0.1.0.1..1.3.1.2..0.1.1.0..3.0.4.0..1.0.2.1
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Oct 05 2012
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