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A218726 a(n) = (23^n-1)/22. 4

%I

%S 0,1,24,553,12720,292561,6728904,154764793,3559590240,81870575521,

%T 1883023236984,43309534450633,996119292364560,22910743724384881,

%U 526947105660852264,12119783430199602073,278755018894590847680,6411365434575589496641

%N a(n) = (23^n-1)/22.

%C Partial sums of powers of 23, q-integers for q=23: diagonal k=1 in triangle A022187.

%C Partial sums are in A014909. Also, the sequence is related to A014941 by A014941 n) = n*a(n)-sum(a(i), i=0..n-1) for n>0. [_Bruno Berselli_, Nov 07 2012]

%H Vincenzo Librandi, <a href="/A218726/b218726.txt">Table of n, a(n) for n = 0..700</a>

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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (24,-23).

%F G.f.: x/((1-x)*(1-23*x)). - _Vincenzo Librandi_, Nov 07 2012

%F a(n) = floor(23^n/22). - _Vincenzo Librandi_, Nov 07 2012

%F a(n) = 24*a(n-1) - 23*a(n-2). - _Vincenzo Librandi_, Nov 07 2012

%t LinearRecurrence[{24, -23}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)

%t (23^Range[0,20]-1)/22 (* _Harvey P. Dale_, Nov 09 2012 *)

%o (PARI) A218726(n)=23^n\22

%o (MAGMA) [n le 2 select n-1 else 24*Self(n-1)-23*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, 07 2012

%o (Maxima) A218726(n):=(23^n-1)/22$

%o makelist(A218726(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

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Last modified July 17 23:21 EDT 2019. Contains 325109 sequences. (Running on oeis4.)