

A140048


a(n) = (1/2)*Sum_{j=0..2^n1} j^(n1) for n>=1.


1



1, 3, 70, 7200, 3098760, 5461682688, 39119789090720, 1134989202339225600, 133147573896710665570432, 63073498348368958240316325888, 120514654247860687784734309977868800
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OFFSET

1,2


COMMENTS

Related to the ProuhetTarryEscott problem.


LINKS



FORMULA

a(n) = Sum_{j=0..2^n1, A010060(j)=0 } j^(n1), n>=1; also,
a(n) = Sum_{j=0..2^n1, A010060(j)=1 } j^(n1), n>=1;
where A010060 is the ThueMorse sequence.


EXAMPLE

For n=3, since A010060(j) = 0 at j={0,3,5,6}, then
a(3) = 0^2 + 3^2 + 5^2 + 6^2 = 70 ;
and since A010060(j) = 1 at j={1,2,4,7}, we also have
a(3) = 1^2 + 2^2 + 4^2 + 7^2 = 70.
For n=4, since A010060(j) = 0 at j={0,3,5,6,9,10,12,15}, then
a(4) = 0^3 + 3^3 + 5^3 + 6^3 + 9^3 + 10^3 + 12^3 + 15^3 = 7200 ;
and since A010060(j) = 1 at j={1,2,4,7,8,11,13,14}, we also have
a(4) = 1^3 + 2^3 + 4^3 + 7^3 + 8^3 + 11^3 + 13^3 + 14^3 = 7200.


PROG

(PARI) a(n)=sum(j=0, 2^n1, j^(n1))/2


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



