cp's OEIS Frontend

A140048 a(n) = (1/2)*Sum_{j=0..2^n-1} j^(n-1) for n>=1.

%I A140048 #2 Mar 30 2012 18:37:10
%S A140048 1,3,70,7200,3098760,5461682688,39119789090720,1134989202339225600,
%T A140048 133147573896710665570432,63073498348368958240316325888,
%U A140048 120514654247860687784734309977868800
%N A140048 a(n) = (1/2)*Sum_{j=0..2^n-1} j^(n-1) for n>=1.
%C A140048 Related to the Prouhet-Tarry-Escott problem.
%F A140048 Main diagonal of triangle A140047.
%F A140048 a(n) = Sum_{j=0..2^n-1, A010060(j)=0 } j^(n-1), n>=1; also,
%F A140048 a(n) = Sum_{j=0..2^n-1, A010060(j)=1 } j^(n-1), n>=1;
%F A140048 where A010060 is the Thue-Morse sequence.
%e A140048 For n=3, since A010060(j) = 0 at j={0,3,5,6}, then
%e A140048 a(3) = 0^2 + 3^2 + 5^2 + 6^2 = 70 ;
%e A140048 and since A010060(j) = 1 at j={1,2,4,7}, we also have
%e A140048 a(3) = 1^2 + 2^2 + 4^2 + 7^2 = 70.
%e A140048 For n=4, since A010060(j) = 0 at j={0,3,5,6,9,10,12,15}, then
%e A140048 a(4) = 0^3 + 3^3 + 5^3 + 6^3 + 9^3 + 10^3 + 12^3 + 15^3 = 7200 ;
%e A140048 and since A010060(j) = 1 at j={1,2,4,7,8,11,13,14}, we also have
%e A140048 a(4) = 1^3 + 2^3 + 4^3 + 7^3 + 8^3 + 11^3 + 13^3 + 14^3 = 7200.
%o A140048 (PARI) a(n)=sum(j=0,2^n-1,j^(n-1))/2
%Y A140048 Cf. A140047; A010060.
%K A140048 nonn
%O A140048 1,2
%A A140048 _Paul D. Hanna_, May 12 2008