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%I #16 Sep 08 2022 08:46:04
%S 0,1,41,1641,65641,2625641,105025641,4201025641,168041025641,
%T 6721641025641,268865641025641,10754625641025641,430185025641025641,
%U 17207401025641025641,688296041025641025641,27531841641025641025641
%N a(n) = (40^n-1)/39.
%C Partial sums of powers of 40 (A009983).
%H Vincenzo Librandi, <a href="/A218743/b218743.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/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (41,-40)
%F a(n) = floor(40^n/39).
%F G.f.: x/((1-x)*(1-40*x)). - _Vincenzo Librandi_, Nov 07 2012
%F a(n) = 41*a(n-1) - 40*a(n-2). - _Vincenzo Librandi_, Nov 07 2012
%t LinearRecurrence[{41, -40}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%o (PARI) a(n)=40^n\39
%o (Maxima) A218743(n):=floor(40^n/39)$ makelist(A218743(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */
%o (Magma) [n le 2 select n-1 else 41*Self(n-1) - 40*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, 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.
%K nonn,easy
%O 0,3
%A _M. F. Hasler_, Nov 04 2012
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