A013724 -id:A013724 - 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]

A013723 a(n) = 18^(2*n + 1).

Original entry on oeis.org

18, 5832, 1889568, 612220032, 198359290368, 64268410079232, 20822964865671168, 6746640616477458432, 2185911559738696531968, 708235345355337676357632, 229468251895129407139872768

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 (324).

Bisection of A001027 (18^n).

Cf. A013708-A013722, A013724-A013729.

[18^(2*n+1): n in [0..15]]; // Vincenzo Librandi, Jun 26 2011

seq(18^(2*n+1),n=0..10); # Nathaniel Johnston, Jun 25 2011

18^(2*Range[0,20]+1) (* or *) NestList[324#&,18,20] (* Harvey P. Dale, Sep 28 2021 *)

a(n)=18^(2*n+1) \\ Charles R Greathouse IV, Jul 11 2016

From Philippe Deléham, Nov 28 2008: (Start)
a(n) = 324*a(n-1); a(0)=18.
G.f.: 18/(1-324*x). (End)

A013725 a(n) = 20^(2*n + 1).

Original entry on oeis.org

20, 8000, 3200000, 1280000000, 512000000000, 204800000000000, 81920000000000000, 32768000000000000000, 13107200000000000000000, 5242880000000000000000000, 2097152000000000000000000000, 838860800000000000000000000000, 335544320000000000000000000000000

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 (400).

Bisection of A009964 (20^n).

Cf. A004171, A005408, A013708-A013724, A013726-A013729.

[20^(2*n+1): n in [0..15]]; // Vincenzo Librandi, Jun 26 2011

seq(20^(2*n+1),n=0..10); # Nathaniel Johnston, Jun 25 2011

NestList[400*# &, 20, 15] (* Paolo Xausa, Jul 12 2025 *)

a(n)=20^(2*n+1) \\ Charles R Greathouse IV, Jul 11 2016

From Philippe Deléham, Nov 28 2008: (Start)
a(n) = 400*a(n-1); a(0)=20.
G.f.: 20/(1-400*x). (End)
From Elmo R. Oliveira, Jul 10 2025: (Start)
E.g.f.: 20*exp(400*x).
a(n) = A004171(n)*A013715(n) = A009964(A005408(n)). (End)

cp's OEIS Frontend

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

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A013723 a(n) = 18^(2*n + 1).

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A013725 a(n) = 20^(2*n + 1).

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