A262716 a(n) = 31^(2*n+1).

31, 29791, 28629151, 27512614111, 26439622160671, 25408476896404831, 24417546297445042591, 23465261991844685929951, 22550116774162743178682911, 21670662219970396194714277471, 20825506393391550743120420649631, 20013311644049280264138724244295391

Offset: 0

Author

Vincenzo Librandi, Oct 07 2015

Keywords

• nonn
• easy

Comments

31*a(n) is a square.

In general, Sum_{i>=0} 1/m^(2*i+1) = m/(m^2-1) when |m|>1. In this case, Sum_{i>=0} 1/a(i) = 31/960. [Bruno Berselli, Oct 07 2015]

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250
• Index entries for linear recurrences with constant coefficients, signature (961).

Crossrefs

Second bisection of A009975 (powers of 31).

Cf. similar sequences listed in A262715.

Programs

Magma

[31^(2*n+1): n in [0..15]];

Mathematica

31^Range[1, 30, 2]

PARI

Vec(31/(1 - 961*x) + O(x^30)) \\ Michel Marcus, Oct 07 2015

PARI

vector(15, n, n--; 31^(2*n+1)) \\ Bruno Berselli, Oct 07 2015

Sage

[31^(2*n+1) for n in (0..15)] # Bruno Berselli, Oct 07 2015

Formula

G.f.: 31/(1 - 961*x).

a(n) = 961*a(n-1).