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

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

Offset

1,2

Comments

Related to the Prouhet-Tarry-Escott problem.

Links

Table of n, a(n) for n=1..11.

Formula

Main diagonal of triangle A140047.

a(n) = Sum_{j=0..2^n-1, A010060(j)=0 } j^(n-1), n>=1; also,

a(n) = Sum_{j=0..2^n-1, A010060(j)=1 } j^(n-1), n>=1;

where A010060 is the Thue-Morse 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^n-1, j^(n-1))/2

Crossrefs

Cf. A140047; A010060.

Sequence in context: A338408 A277413 A210920 * A135951 A361254 A093245

Adjacent sequences: A140045 A140046 A140047 * A140049 A140050 A140051

Keyword

nonn

Author

Paul D. Hanna, May 12 2008

Status

approved