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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Sum over the inverse squares of A016777. Dirichlet series Sum_{n>=1} A079978(n-1)/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 (* Jean-François 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 Jean-François Alcover, Feb 11 2013

STATUS

approved

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Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)