A086727 -id:A086727 - cp's OEIS frontend

A016922 a(n) = (6*n+1)^2.

1, 49, 169, 361, 625, 961, 1369, 1849, 2401, 3025, 3721, 4489, 5329, 6241, 7225, 8281, 9409, 10609, 11881, 13225, 14641, 16129, 17689, 19321, 21025, 22801, 24649, 26569, 28561, 30625, 32761, 34969, 37249, 39601, 42025, 44521, 47089, 49729, 52441, 55225

Offset: 0

N. J. A. Sloane

Except for 2, exponents e such that x^e-x+1 is reducible.

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

Cf. A000290, A005449, A086727, A016778 (bisection), A016921.

[(6*n+1)^2: n in [0..60]]; // Vincenzo Librandi, May 04 2011

A016922:=n->(6*n+1)^2; seq(A016922(n), n=0..100); # Wesley Ivan Hurt, Dec 06 2013

Table[(6n+1)^2, {n,0,100}] (* or *)
CoefficientList[Series[(1 + 46*x + 25*x^2)/(1 - x)^3, {x, 0, 30}], x] (* Wesley Ivan Hurt, Oct 13 2014 *)
LinearRecurrence[{3,-3,1},{1,49,169},50] (* Harvey P. Dale, Feb 17 2023 *)

a(n)=(6*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

G.f.: ( 1+46*x+25*x^2 ) / (1-x)^3. - R. J. Mathar, Mar 10 2011
a(n) = A016921(n)^2 = A000290(A016921(n)). - Wesley Ivan Hurt, Dec 06 2013
a(n) = 24*A005449(n)+1. - Jean-Bernard François, Oct 12 2014
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Wesley Ivan Hurt, Oct 13 2014
Sum_{n>=0} 1/a(n) = A086727. - Amiram Eldar, Nov 16 2020

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

cp's OEIS Frontend

A016922 a(n) = (6*n+1)^2.

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