login
a(n) = (35^n - 1)/34.
4

%I #21 Mar 29 2023 09:02:31

%S 0,1,36,1261,44136,1544761,54066636,1892332261,66231629136,

%T 2318107019761,81133745691636,2839681099207261,99388838472254136,

%U 3478609346528894761,121751327128511316636,4261296449497896082261,149145375732426362879136,5220088150634922700769761

%N a(n) = (35^n - 1)/34.

%C Partial sums of powers of 35 (A009979).

%H Vincenzo Librandi, <a href="/A218738/b218738.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 (36,-35).

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

%F G.f.: x/((1 - x)*(1 - 35*x)).

%F a(n) = 36*a(n-1) - 35*a(n-2).

%F a(n) = floor(35^n/34). (End)

%F E.g.f.: exp(x)*(exp(34*x) - 1)/34. - _Stefano Spezia_, Mar 28 2023

%t LinearRecurrence[{36, -35}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)

%o (PARI) A218738(n)=35^n\34

%o (Magma) [n le 2 select n-1 else 36*Self(n-1)-35*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012

%o (Maxima) A218738(n):=(35^n-1)/34$

%o makelist(A218738(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.

%Y Cf. A009979.

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, Nov 04 2012