login
a(n) = (34^n - 1)/33.
4

%I #20 Mar 26 2023 10:29:29

%S 0,1,35,1191,40495,1376831,46812255,1591616671,54114966815,

%T 1839908871711,62556901638175,2126934655697951,72315778293730335,

%U 2458736461986831391,83597039707552267295,2842299350056777088031,96638177901930420993055,3285698048665634313763871

%N a(n) = (34^n - 1)/33.

%C Partial sums of powers of 34 (A009978).

%H Vincenzo Librandi, <a href="/A218737/b218737.txt">Table of n, a(n) for n = 0..600</a>

%H <a href="/index/Par#partial">Index entries related to partial sums</a>.

%H <a href="/index/Q#q-numbers">Index entries related to q-numbers</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (35,-34).

%F From _Vincenzo Librandi_, Nov 07 2012: (Start)

%F G.f.: x/((1 - x)*(1 - 34*x)).

%F a(n) = 35*a(n-1) - 34*a(n-2).

%F a(n) = floor(34^n/33). (End)

%F E.g.f.: exp(x)*(exp(33*x) - 1)/33. - _Stefano Spezia_, Mar 26 2023

%t LinearRecurrence[{35, -34}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)

%o (PARI) A218737(n)=34^n\33

%o (Magma) [n le 2 select n-1 else 35*Self(n-1)-34*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012

%o (Maxima) A218737(n):=(34^n-1)/33$

%o makelist(A218737(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */

%Y Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, Nov 04 2012