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A218733 a(n) = (30^n - 1)/29.

%I A218733 #28 Aug 29 2024 17:51:27
%S A218733 0,1,31,931,27931,837931,25137931,754137931,22624137931,678724137931,
%T A218733 20361724137931,610851724137931,18325551724137931,549766551724137931,
%U A218733 16492996551724137931,494789896551724137931,14843696896551724137931,445310906896551724137931,13359327206896551724137931
%N A218733 a(n) = (30^n - 1)/29.
%C A218733 Partial sums of powers of 30 (A009974).
%H A218733 Vincenzo Librandi, <a href="/A218733/b218733.txt">Table of n, a(n) for n = 0..600</a>
%H A218733 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218733 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (31,-30).
%F A218733 a(n) = floor(30^n/29).
%F A218733 From _Vincenzo Librandi_, Nov 07 2012: (Start)
%F A218733 G.f.: x/((1-x)*(1-30*x)).
%F A218733 a(n) = 31*a(n-1) - 30*a(n-2). (End)
%F A218733 E.g.f.: exp(x)*(exp(29*x) - 1)/29. - _Elmo R. Oliveira_, Aug 29 2024
%t A218733 LinearRecurrence[{31, -30}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%t A218733 (30^Range[0,20]-1)/29 (* _Harvey P. Dale_, Nov 22 2022 *)
%o A218733 (PARI) A218733(n)=30^n\29
%o A218733 (Maxima) A218733(n):=floor((30^n-1)/29)$ makelist(A218733(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */
%o A218733 (Magma) [n le 2 select n-1 else 31*Self(n-1) - 30*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%Y A218733 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 A218733 Cf. A009974.
%K A218733 nonn,easy
%O A218733 0,3
%A A218733 _M. F. Hasler_, Nov 04 2012