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%I #11 Mar 27 2021 01:00:39
%S 1,2,2,1,2,1,1,1,2,5,2,1,5,5,1,1,2,1,1,2,1,2,8,8,2,1,8,15,8,1,2,8,8,2,
%T 1,2,1,1,3,3,1,2,11,18,11,2,1,11,31,31,11,1,3,18,31,18,3,3,11,11,3,1,
%U 2,1,1,4,6,4,1,2,14,32,32,14,2,1,14,53,80,53,14,1,4,32,80,80,32,4,6
%N Entries in 3-dimensional solid related to Prouhet-Tarry problem.
%C Entries of slices [2,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, slice [1,k] gives A109393.
%F Sum of terms in 2D slice [2, k] is 3^(2+k).
%e Slice [2,0]:
%e .... 1 ....
%e ... 2 2 ...
%e .. 1 2 1 ...
%e Slice [2,1]:
%e .... 1 1 ....
%e ... 2 5 2 ...
%e .. 1 5 5 1 ...
%e ... 1 2 1 ...
%e Slice [2,2]:
%e .... 1 2 1 ....
%e ... 2 8 8 2 ...
%e .. 1 8 15 8 1 ...
%e ... 2 8 8 2 ...
%e .... 1 2 1 ....
%e Slice [2,3]:
%e .... 1 3 3 1 ....
%e ... 2 11 18 11 2 ...
%e .. 1 11 31 31 11 1 ...
%e ... 3 18 31 18 3 ....
%e .... 3 11 11 3 .....
%e ..... 1 2 1 ......
%e Slice [2,4]:
%e .... 1 4 6 4 1 ...
%e ... 2 14 32 32 14 2 ...
%e .. 1 14 53 80 53 14 1 ...
%e ... 4 32 80 80 32 4 ....
%e .... 6 32 53 32 6 .....
%e ..... 4 14 14 4 .....;
%e ...... 1 2 1 ......;
%e Slice [2,5]:
%e .... 1 5 10 10 5 1 ...
%e ... 2 17 50 70 50 17 2 ...
%e .. 1 17 81 165 165 81 17 1 ...
%e ... 5 50 165 240 165 50 5 ....
%e .... 10 70 165 165 70 10 .....
%e ..... 10 50 81 50 10 ......
%e ...... 5 17 17 5 ......
%e ....... 1 2 1 .......
%Y Cf. A109672, A046816, A109649, A109673, A109390, A109393.
%K nonn,tabf,easy
%O 0,2
%A _Philippe Deléham_, Aug 29 2005