A217510 - OEIS

%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