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a(n) = (30^n - 1)/29.
6

%I #28 Aug 29 2024 17:51:27

%S 0,1,31,931,27931,837931,25137931,754137931,22624137931,678724137931,

%T 20361724137931,610851724137931,18325551724137931,549766551724137931,

%U 16492996551724137931,494789896551724137931,14843696896551724137931,445310906896551724137931,13359327206896551724137931

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

%C Partial sums of powers of 30 (A009974).

%H Vincenzo Librandi, <a href="/A218733/b218733.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/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (31,-30).

%F a(n) = floor(30^n/29).

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

%F G.f.: x/((1-x)*(1-30*x)).

%F a(n) = 31*a(n-1) - 30*a(n-2). (End)

%F E.g.f.: exp(x)*(exp(29*x) - 1)/29. - _Elmo R. Oliveira_, Aug 29 2024

%t LinearRecurrence[{31, -30}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)

%t (30^Range[0,20]-1)/29 (* _Harvey P. Dale_, Nov 22 2022 *)

%o (PARI) A218733(n)=30^n\29

%o (Maxima) A218733(n):=floor((30^n-1)/29)$ makelist(A218733(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */

%o (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 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. A009974.

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, Nov 04 2012