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%I #19 Mar 24 2023 18:32:54
%S 0,1,34,1123,37060,1222981,40358374,1331826343,43950269320,
%T 1450358887561,47861843289514,1579440828553963,52121547342280780,
%U 1720011062295265741,56760365055743769454,1873092046839544391983,61812037545704964935440,2039797239008263842869521
%N a(n) = (33^n - 1)/32.
%C Partial sums of powers of 33 (A009977).
%H Vincenzo Librandi, <a href="/A218736/b218736.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/Q#q-numbers">Index entries related to q-numbers</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (34,-33).
%F From _Vincenzo Librandi_, Nov 07 2012: (Start)
%F G.f.: x/((1 - x)*(1 - 33*x)).
%F a(n) = 34*a(n-1) - 33*a(n-2).
%F a(n) = floor(33^n/32). (End)
%F E.g.f.: exp(x)*(exp(32*x) - 1)/32. - _Stefano Spezia_, Mar 24 2023
%t LinearRecurrence[{34, -33}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%o (PARI) A218736(n)=33^n>>5
%o (Magma) [n le 2 select n-1 else 34*Self(n-1)-33*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o (Maxima) A218736(n):=(33^n-1)/32$
%o makelist(A218736(n),n,0,30); /* _Martin Ettl_, Nov 05 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, A218737-A218753, A133853, A094028, A218723.
%K nonn,easy
%O 0,3
%A _M. F. Hasler_, Nov 04 2012
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