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%I #8 Sep 08 2013 13:30:46
%S 1,1,1,1,3,1,1,1,1,2,1,2,8,8,2,1,8,15,8,1,2,8,8,2,1,2,1,1,3,3,1,3,15,
%T 24,15,3,3,24,60,60,24,3,1,15,60,93,60,15,1,3,24,60,60,24,3,3,15,24,
%U 15,3,1,3,3,1,1,4,6,4,1,4,24,52,52,24,4,6,52,160,228,160,52,6,4,52
%N Hexagonal pyramid related to Prouhet-Tarry problem.
%C Entries of slices [n,n] in A109672, read by rows.
%C Greatest numbers in each slice (central numbers) form A002893 : 1, 3, 15, 93, 639, ...
%F Sum of terms in slice [n, n] = 3^(2n); example : 1+2+1+2+8+15+8+1+2+8+8+2+1+2+1 = 3^4 = 81 for the slice [2, 2].
%e Slice [0, 0]:
%e ... 1 ...
%e Slice [1,1]:
%e ... 1 1 ...
%e .. 1 3 1 ...
%e ... 1 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 [3,3]:
%e ...... 1 3 3 1 .....
%e .... 3 15 24 15 3 ...
%e ... 3 24 60 60 24 3 ...
%e .. 1 15 60 93 60 15 1 ...
%e ... 3 24 60 60 24 3 ...
%e .... 3 15 24 15 3 ....
%e ...... 1 3 3 1 ....
%K nonn,tabf,easy
%O 0,5
%A _Philippe Deléham_, Aug 07 2005