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A218740 a(n) = (37^n - 1)/36.

%I A218740 #19 Mar 28 2023 17:47:32
%S A218740 0,1,38,1407,52060,1926221,71270178,2636996587,97568873720,
%T A218740 3610048327641,133571788122718,4942156160540567,182859777940000980,
%U A218740 6765811783780036261,250335035999861341658,9262396331994869641347,342708664283810176729840,12680220578500976539004081
%N A218740 a(n) = (37^n - 1)/36.
%C A218740 Partial sums of powers of 37 (A009981).
%H A218740 Vincenzo Librandi, <a href="/A218740/b218740.txt">Table of n, a(n) for n = 0..600</a>
%H A218740 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218740 <a href="/index/Q#q-numbers">Index entries related to q-numbers</a>.
%H A218740 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (38,-37).
%F A218740 From _Vincenzo Librandi_, Nov 07 2012: (Start)
%F A218740 G.f.: x/((1 - x)*(1 - 37*x)).
%F A218740 a(n) = 38*a(n-1) - 37*a(n-2).
%F A218740 a(n) = floor(37^n/36). (End)
%F A218740 E.g.f.: exp(x)*(exp(36*x) - 1)/36. - _Stefano Spezia_, Mar 28 2023
%t A218740 LinearRecurrence[{38, -37}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%o A218740 (PARI) A218740(n)=37^n\36
%o A218740 (Magma) [n le 2 select n-1 else 38*Self(n-1)-37*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o A218740 (Maxima) A218740(n):=(37^n-1)/36$
%o A218740 makelist(A218740(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%Y A218740 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 A218740 Cf. A009981.
%K A218740 nonn,easy
%O A218740 0,3
%A A218740 _M. F. Hasler_, Nov 04 2012