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A218749 a(n) = (46^n - 1)/45.

%I A218749 #30 Aug 29 2024 19:56:39
%S A218749 0,1,47,2163,99499,4576955,210539931,9684836827,445502494043,
%T A218749 20493114725979,942683277395035,43363430760171611,1994717814967894107,
%U A218749 91757019488523128923,4220822896472063930459,194157853237714940801115,8931261248934887276851291,410838017451004814735159387
%N A218749 a(n) = (46^n - 1)/45.
%C A218749 Partial sums of powers of 46 (A009990).
%H A218749 Vincenzo Librandi, <a href="/A218749/b218749.txt">Table of n, a(n) for n = 0..600</a>
%H A218749 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218749 <a href="/index/Q#q-numbers">Index entries related to q-numbers</a>.
%H A218749 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (47,-46).
%F A218749 From _Vincenzo Librandi_, Nov 08 2012: (Start)
%F A218749 G.f.: x/((1-x)*(1-46*x)).
%F A218749 a(n) = 47*a(n-1) - 46*a(n-2) with a(0)=0, a(1)=1.
%F A218749 a(n) = 46*a(n-1) + 1 with a(0)=0.
%F A218749 a(n) = floor(46^n/45). (End)
%F A218749 E.g.f.: exp(x)*(exp(45*x) - 1)/45. - _Elmo R. Oliveira_, Aug 29 2024
%t A218749 LinearRecurrence[{47, -46}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 08 2012 *)
%t A218749 (46^Range[0,20]-1)/45 (* _Harvey P. Dale_, Aug 17 2017 *)
%o A218749 (PARI) A218749(n)=46^n\45
%o A218749 (Maxima) A218749(n):=(46^n-1)/45$ makelist(A218749(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%o A218749 (Magma) [n le 2 select n-1 else 47*Self(n-1) - 46*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 08 2012
%Y A218749 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 A218749 Cf. A009990.
%K A218749 nonn,easy
%O A218749 0,3
%A A218749 _M. F. Hasler_, Nov 04 2012