This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A218726 #26 Aug 03 2025 00:05:45
%S A218726 0,1,24,553,12720,292561,6728904,154764793,3559590240,81870575521,
%T A218726 1883023236984,43309534450633,996119292364560,22910743724384881,
%U A218726 526947105660852264,12119783430199602073,278755018894590847680,6411365434575589496641,147461404995238558422744
%N A218726 a(n) = (23^n - 1)/22.
%C A218726 Partial sums of powers of 23, q-integers for q=23: diagonal k=1 in triangle A022187.
%C A218726 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 A218726 Vincenzo Librandi, <a href="/A218726/b218726.txt">Table of n, a(n) for n = 0..700</a>
%H A218726 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218726 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (24,-23).
%F A218726 From _Vincenzo Librandi_, Nov 07 2012: (Start)
%F A218726 G.f.: x/((1-x)*(1-23*x)).
%F A218726 a(n) = floor(23^n/22).
%F A218726 a(n) = 24*a(n-1) - 23*a(n-2). (End)
%F A218726 E.g.f.: exp(12*x)*sinh(11*x)/11. - _Elmo R. Oliveira_, Aug 27 2024
%t A218726 LinearRecurrence[{24, -23}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%t A218726 (23^Range[0,20]-1)/22 (* _Harvey P. Dale_, Nov 09 2012 *)
%o A218726 (PARI) A218726(n)=23^n\22
%o A218726 (Magma) [n le 2 select n-1 else 24*Self(n-1)-23*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o A218726 (Maxima) A218726(n):=(23^n-1)/22$
%o A218726 makelist(A218726(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%Y A218726 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 A218726 Cf. A014909, A014941, A022187.
%K A218726 nonn,easy
%O A218726 0,3
%A A218726 _M. F. Hasler_, Nov 04 2012