A013718 -id:A013718 - cp's OEIS frontend

A262715 a(n) = 29^(2*n+1).

29, 24389, 20511149, 17249876309, 14507145975869, 12200509765705829, 10260628712958602189, 8629188747598184440949, 7257147736730073114838109, 6103261246589991489578849669, 5132842708382182842735812571629, 4316720717749415770740818372739989

Offset: 0

Vincenzo Librandi, Oct 02 2015

29*a(n) is a square.

G. C. Greubel, Table of n, a(n) for n = 0..250
Index entries for linear recurrences with constant coefficients, signature (841).

Second bisection of A009973 (powers of 29).

Cf. similar sequences of the form p^(2*n+1), with p prime: A004171 (p=2), A013708 (p=3), A013710 (p=5), A013712 (p=7), A013716 (p=11), A013718 (p=13), A013722 (p=17), A013724 (p=19), A013728 (p=23), this sequence (p=29), A262716 (p=31), A262786 (p=37), A262787 (p=41), A155477 (p=43).

Magma
```
[29^(2*n+1): n in [0..15]];
```

29^Range[1, 30, 2]
NestList[841#&,29,20] (* Harvey P. Dale, May 16 2025 *)

vector(20, n, n--; 29^(2*n+1)) \\ Altug Alkan, Oct 02 2015

G.f.: 29/(1 - 841*x).
a(n) = 841*a(n-1).
Sum_{i>=0} (-1)^i/a(i) = 29*A021846; Sum_{i>=0} 1/a(i) = 2.9*A021088. [Bruno Berselli, Oct 06 2015]

A013717 a(n) = 12^(2*n + 1).

Original entry on oeis.org

12, 1728, 248832, 35831808, 5159780352, 743008370688, 106993205379072, 15407021574586368, 2218611106740436992, 319479999370622926848, 46005119909369701466112, 6624737266949237011120128

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (144).

Bisection of A001021.

Cf. A013708-A013716, A013718-A013729.

[12^(2*n+1): n in [0..15]]; // Vincenzo Librandi, Jun 26 2011

seq(12^(2*n+1),n=0..11); # Nathaniel Johnston, Jun 25 2011

a(n)=12^(2*n+1) \\ Charles R Greathouse IV, Jul 11 2016

From Philippe Deléham, Nov 25 2008: (Start)
a(n) = 144*a(n-1), a(0)=12.
G.f.: 12/(1-144*x). (End)

A013719 a(n) = 14^(2*n + 1).

Original entry on oeis.org

14, 2744, 537824, 105413504, 20661046784, 4049565169664, 793714773254144, 155568095557812224, 30491346729331195904, 5976303958948914397184, 1171355575953987221848064, 229585692886981495482220544

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (196).

Bisection of A001023 (14^n).

Cf. A013708-A013718, A013720-A013729.

[14^(2*n+1): n in [0..15]]; // Vincenzo Librandi, Jun 26 2011

seq(14^(2*n+1),n=0..11); # Nathaniel Johnston, Jun 25 2011

a(n)=14^(2*n+1) \\ Charles R Greathouse IV, Jul 11 2016

From Philippe Deléham, Nov 25 2008: (Start)
a(n) = 196*a(n-1), a(0)=14.
G.f.: 14/(1-196*x). (End)

cp's OEIS Frontend

A262715 a(n) = 29^(2*n+1).

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A013717 a(n) = 12^(2*n + 1).

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A013719 a(n) = 14^(2*n + 1).

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