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a(n) = (27^n - 1)/26.
3

%I #20 Aug 27 2024 22:21:38

%S 0,1,28,757,20440,551881,14900788,402321277,10862674480,293292210961,

%T 7918889695948,213810021790597,5772870588346120,155867505885345241,

%U 4208422658904321508,113627411790416680717,3067940118341250379360,82834383195213760242721,2236528346270771526553468

%N a(n) = (27^n - 1)/26.

%C Partial sums of powers of 27 (A009971); q-integers for q=27.

%H Vincenzo Librandi, <a href="/A218730/b218730.txt">Table of n, a(n) for n = 0..700</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 (28,-27).

%F G.f.: x/((1-x)*(1-27*x)). - _Vincenzo Librandi_, Nov 07 2012

%F a(n) = floor(27^n/26). - _Vincenzo Librandi_, Nov 07 2012

%F a(n) = 28*a(n-1) - 27*a(n-2). - _Vincenzo Librandi_, Nov 07 2012

%F E.g.f.: exp(14*x)*sinh(13*x)/13. - _Elmo R. Oliveira_, Aug 27 2024

%t LinearRecurrence[{28, -27}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)

%o (PARI) a(n)=27^n\26

%o (Magma) [n le 2 select n-1 else 28*Self(n-1)-27*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012

%o (Maxima) A218730(n):=(27^n-1)/26$

%o makelist(A218730(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. A009971.

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, Nov 04 2012