A059723 Mean of the first 2^n nonnegative powers of 3, i.e., (1 + 3 + 3^2 + ... + 3^(2^n-1))/2^n.

1, 2, 10, 410, 1345210, 28953440450810, 26825654846035253786389446010, 46055408506791340513753409614892651037805514032327504332410

Offset: 0

Author

Henry Bottomley, Feb 07 2001

Keywords

• nonn

Examples

			a(3) = (1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187)/8 = 3280/8 = 410.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..11
• N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]

Crossrefs

Cf. A059721, A059722.

Programs

PARI

{ for (n=0, 11, write("b059723.txt", n, " ", (3^(2^n) - 1)/2^(n + 1)); ) } \\ Harry J. Smith, Jun 28 2009

Formula

a(n) = (3^(2^n) - 1)/2^(n+1).