A262716 - OEIS

%I #15 Sep 08 2022 08:46:14

%S 31,29791,28629151,27512614111,26439622160671,25408476896404831,

%T 24417546297445042591,23465261991844685929951,

%U 22550116774162743178682911,21670662219970396194714277471,20825506393391550743120420649631,20013311644049280264138724244295391

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

%C 31*a(n) is a square.

%C 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]

%H G. C. Greubel, <a href="/A262716/b262716.txt">Table of n, a(n) for n = 0..250</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (961).

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

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

%t 31^Range[1, 30, 2]

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

%o (PARI) Vec(31/(1 - 961*x) + O(x^30)) \\ _Michel Marcus_, Oct 07 2015

%o (PARI) vector(15, n, n--; 31^(2*n+1)) \\ _Bruno Berselli_, Oct 07 2015

%o (Sage) [31^(2*n+1) for n in (0..15)] # _Bruno Berselli_, Oct 07 2015

%Y Second bisection of A009975 (powers of 31).

%Y Cf. similar sequences listed in A262715.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Oct 07 2015