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a(n) = (36^n - 1)/35.
3

%I #22 Mar 29 2023 09:02:23

%S 0,1,37,1333,47989,1727605,62193781,2238976117,80603140213,

%T 2901713047669,104461669716085,3760620109779061,135382323952046197,

%U 4873763662273663093,175455491841851871349,6316397706306667368565,227390317427040025268341,8186051427373440909660277

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

%C Partial sums of powers of 36 (A009980).

%H Vincenzo Librandi, <a href="/A218739/b218739.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 (37,-36).

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

%F G.f.: x/((1 - x)*(1 - 36*x)).

%F a(n) = 37*a(n-1) - 36*a(n-2).

%F a(n) = floor(36^n/35). (End)

%F E.g.f.: exp(x)*(exp(35*x) - 1)/35. - _Stefano Spezia_, Mar 28 2023

%t LinearRecurrence[{37, -36}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)

%t Join[{0},Accumulate[36^Range[0,20]]] (* _Harvey P. Dale_, Jun 03 2015 *)

%o (PARI) A218739(n)=36^n\35

%o (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 (Maxima) A218739(n):=(36^n-1)/35$

%o makelist(A218739(n),n,0,30); /* _Martin Ettl_, 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. A009980.

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, Nov 04 2012