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A218731 a(n) = (28^n - 1)/27.

%I A218731 #19 Aug 29 2024 17:44:12
%S A218731 0,1,29,813,22765,637421,17847789,499738093,13992666605,391794664941,
%T A218731 10970250618349,307167017313773,8600676484785645,240818941573998061,
%U A218731 6742930364071945709,188802050194014479853,5286457405432405435885,148020807352107352204781,4144582605859005861733869
%N A218731 a(n) = (28^n - 1)/27.
%C A218731 Partial sums of powers of 28 (A009972).
%H A218731 Vincenzo Librandi, <a href="/A218731/b218731.txt">Table of n, a(n) for n = 0..700</a>
%H A218731 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218731 <a href="/index/Q#q-numbers">Index entries related to q-numbers</a>.
%H A218731 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (29,-28).
%F A218731 From _Vincenzo Librandi_, Nov 07 2012: (Start)
%F A218731 G.f.: x/((1-x)*(1-28*x)).
%F A218731 a(n) = floor(28^n/27).
%F A218731 a(n) = 29*a(n-1) - 28*a(n-2). (End)
%F A218731 E.g.f.: exp(x)*(exp(27*x) - 1)/27. - _Elmo R. Oliveira_, Aug 29 2024
%t A218731 LinearRecurrence[{29, -28}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%o A218731 (PARI) A218731(n)=28^n\27
%o A218731 (Magma) [n le 2 select n-1 else 29*Self(n-1)-28*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o A218731 (Maxima) A218731(n):=(28^n-1)/27$
%o A218731 makelist(A218731(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%Y A218731 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 A218731 Cf. A009972.
%K A218731 nonn,easy
%O A218731 0,3
%A A218731 _M. F. Hasler_, Nov 04 2012