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 A140048 a(n) = (1/2)*Sum_{j=0..2^n-1} j^(n-1) for n>=1. 1
 1, 3, 70, 7200, 3098760, 5461682688, 39119789090720, 1134989202339225600, 133147573896710665570432, 63073498348368958240316325888, 120514654247860687784734309977868800 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 3 05:03 EST 2023. Contains 367531 sequences. (Running on oeis4.)