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A218739 a(n) = (36^n - 1)/35.

%I A218739 #22 Mar 29 2023 09:02:23
%S A218739 0,1,37,1333,47989,1727605,62193781,2238976117,80603140213,
%T A218739 2901713047669,104461669716085,3760620109779061,135382323952046197,
%U A218739 4873763662273663093,175455491841851871349,6316397706306667368565,227390317427040025268341,8186051427373440909660277
%N A218739 a(n) = (36^n - 1)/35.
%C A218739 Partial sums of powers of 36 (A009980).
%H A218739 Vincenzo Librandi, <a href="/A218739/b218739.txt">Table of n, a(n) for n = 0..600</a>
%H A218739 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218739 <a href="/index/Q#q-numbers">Index entries related to q-numbers</a>.
%H A218739 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (37,-36).
%F A218739 From _Vincenzo Librandi_, Nov 07 2012: (Start)
%F A218739 G.f.: x/((1 - x)*(1 - 36*x)).
%F A218739 a(n) = 37*a(n-1) - 36*a(n-2).
%F A218739 a(n) = floor(36^n/35). (End)
%F A218739 E.g.f.: exp(x)*(exp(35*x) - 1)/35. - _Stefano Spezia_, Mar 28 2023
%t A218739 LinearRecurrence[{37, -36}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%t A218739 Join[{0},Accumulate[36^Range[0,20]]] (* _Harvey P. Dale_, Jun 03 2015 *)
%o A218739 (PARI) A218739(n)=36^n\35
%o A218739 (Magma) [n le 2 select n-1 else 37*Self(n-1)-36*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o A218739 (Maxima) A218739(n):=(36^n-1)/35$
%o A218739 makelist(A218739(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%Y A218739 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 A218739 Cf. A009980.
%K A218739 nonn,easy
%O A218739 0,3
%A A218739 _M. F. Hasler_, Nov 04 2012