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%I #8 Sep 08 2013 13:30:45
%S 1,1,1,1,1,1,3,1,1,1,1,2,1,1,5,5,1,2,5,2,1,1,1,3,3,1,1,7,12,7,1,3,12,
%T 12,3,3,7,3,1,1,1,4,6,4,1,1,9,22,22,9,1,4,22,36,22,4,6,22,22,6,4,9,4,
%U 1,1,1,5,10,10,5,1,1,11,35,50,35,11,1,5,35,80,80,35,5,10,50,80,50
%N Entries in 3-dimensional solid related to Prouhet-Tarry problem.
%C Entries of slices [1,k] in A109672, read by rows.
%C Slice [n,0] gives A046816, slice [0,k] gives A109649, slice [n,n] gives A109673, slice [n,1] gives A109390.
%F Sum of terms in 2D slice [1, k] is 3^(1+k).
%e Slice [1,0]:
%e ... 1 ...
%e .. 1 1 ...
%e Slice [1,1]:
%e ... 1 1 ...
%e .. 1 3 1 ...
%e ... 1 1 ...
%e Slice [1,2]:
%e ... 1 2 1 ...
%e .. 1 5 5 1 ...
%e ... 2 5 2 ...
%e .... 1 1 ....
%e Slice [1,3]:
%e ... 1 3 3 1 ...
%e .. 1 7 12 7 1 ...
%e ... 3 12 12 3 ...
%e .... 3 7 3 ....
%e ..... 1 1 .....
%e Slice [1,4]:
%e ... 1 4 6 4 1 ...
%e .. 1 9 22 22 9 1 ...
%e ... 4 22 36 22 4 ...
%e .... 6 22 22 6 ....
%e ..... 4 9 4 .....
%e ...... 1 1 ......
%e Slice [1,5]:
%e ... 1 5 10 10 5 1 ...
%e .. 1 11 35 50 35 11 1 ...
%e ... 5 35 80 80 35 5 ...
%e .... 10 50 80 50 10 ....
%e ..... 10 35 35 10 .....
%e ...... 5 11 5 ......
%e ....... 1 1
%Y Cf. A109390.
%K nonn,tabf,easy
%O 0,7
%A _Philippe Deléham_, Aug 26 2005
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