

A214550


Decimal expansion of Sum_{n>=0} 1/(3n+1)^2.


7



1, 1, 2, 1, 7, 3, 3, 0, 1, 3, 9, 3, 6, 3, 4, 3, 7, 8, 6, 8, 6, 5, 7, 7, 8, 2, 3, 3, 3, 2, 1, 3, 9, 0, 7, 0, 6, 7, 2, 4, 3, 2, 2, 6, 7, 9, 9, 2, 0, 1, 0, 8, 6, 8, 2, 4, 3, 7, 9, 6, 4, 8, 0, 0, 0, 9, 2, 3, 3, 5, 7, 0, 1, 3, 9, 3, 8, 9, 8, 3, 8, 6, 3, 0, 5, 8, 2, 5, 4, 0, 7, 9, 1, 3, 7, 7, 5, 4, 6, 6, 2, 0, 1, 1, 8
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OFFSET

1,3


COMMENTS

Sum over the inverse squares of A016777. Dirichlet series Sum_{n>=1} A079978(n1)/n^s at s=2.
This is also (1/9)*Zeta(2, 1/3) = (1/9)*Psi(1, 1/3) with the Hurwitz Zeta Function Zeta(s, a) and the Polygamma function Psi(n, z). See the programs.  Wolfdieter Lang, Nov 12 2017


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Hurwitz Zeta Function .
Eric Weisstein's World of Mathematics, Polygamma Function.


FORMULA

Equals (A086724 + A214549) /2 because the sequence represented by A079978 (with offset 1) is the average of A011655 and A102283.


EXAMPLE

1.1217330139363437868657... = 1/1^2 + 1/4^2 + 1/7^2 + 1/10^2 + 1/13^2 + ...


MAPLE

evalf(Psi(1, 1/3)/9) ;


MATHEMATICA

RealDigits[ PolyGamma[1, 1/3]/9, 10, 105] // First (* JeanFrançois Alcover, Feb 11 2013 *)


PROG

(PARI) zetahurwitz(2, 1/3)/9 \\ Charles R Greathouse IV, Jan 30 2018
(PARI) sumpos(n=0, 1/(3*n+1)^2) \\ Charles R Greathouse IV, Jan 30 2018


CROSSREFS

Sequence in context: A091370 A125697 A090699 * A120903 A180335 A257699
Adjacent sequences: A214547 A214548 A214549 * A214551 A214552 A214553


KEYWORD

cons,nonn


AUTHOR

R. J. Mathar, Jul 20 2012


EXTENSIONS

More terms from JeanFrançois Alcover, Feb 11 2013


STATUS

approved



