A086728 -id:A086728 - cp's OEIS frontend

A016934 a(n) = (6*n + 2)^2.

4, 64, 196, 400, 676, 1024, 1444, 1936, 2500, 3136, 3844, 4624, 5476, 6400, 7396, 8464, 9604, 10816, 12100, 13456, 14884, 16384, 17956, 19600, 21316, 23104, 24964, 26896, 28900, 30976, 33124, 35344, 37636, 40000, 42436, 44944, 47524, 50176, 52900, 55696, 58564

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A016922, A016933, A086728.

[(6*n+2)^2: n in [0..50]]; // Vincenzo Librandi, May 04 2011

(6*Range[0,40]+2)^2 (* or *) LinearRecurrence[{3,-3,1},{4,64,196},40] (* Harvey P. Dale, Nov 22 2013 *)

a(n)=(6*n+2)^2 \\ Charles R Greathouse IV, Jun 17 2017

Sum_{n>=0} 1/a(n) = A086728. - Amiram Eldar, Nov 16 2020
From Stefano Spezia, Feb 21 2025: (Start)
G.f.: 4*(1 + 13*x + 4*x^2)/(1 - x)^3.
E.g.f.: 4*exp(x)*(1 + 15*x + 9*x^2). (End)

A086729 Decimal expansion of Pi^2/72.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Jul 31 2003

The original name was: Decimal expansion of Sum_{m=0..infinity} 1/(6*m+3)^2.

			0.1370778389040188697...

L. Fejes Toth, Lagerungen in der Ebene, auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972; see p. 213.

Index entries for transcendental numbers

Cf. A086722, A086723, A086724, A086725, A086726, A086727, A086728, A086730, A086731, A111003, A353908.

evalf(Pi^2/72) ;  # R. J. Mathar, Dec 18 2010

PARI
```
Pi^2/72 \\ Omar E. Pol, May 12 2022
```

Equals A111003/9. - R. J. Mathar, Dec 18 2010
From Amiram Eldar, Jul 19 2020: (Start)
Sum_{k>=0} (1/(12*k+3)^2 + 1/(12*k+9)^2).
Equals Integral_{x=1..oo} log(1 + 1/x^6)/x dx. (End)
Equals A353908/2. - Omar E. Pol, May 12 2022

New name after R. J. Mathar's Maple program. - Omar E. Pol, May 12 2022

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A016934 a(n) = (6*n + 2)^2.

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A086729 Decimal expansion of Pi^2/72.

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