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A218750 a(n) = (47^n - 1)/46.

%I A218750 #37 Aug 27 2024 18:18:26
%S A218750 0,1,48,2257,106080,4985761,234330768,11013546097,517636666560,
%T A218750 24328923328321,1143459396431088,53742591632261137,
%U A218750 2525901806716273440,118717384915664851681,5579717091036248029008,262246703278703657363377,12325595054099071896078720
%N A218750 a(n) = (47^n - 1)/46.
%C A218750 Partial sums of powers of 47 (A009991).
%H A218750 Vincenzo Librandi, <a href="/A218750/b218750.txt">Table of n, a(n) for n = 0..600</a>
%H A218750 <a href="/index/Par#partial">Index entries related to partial sums</a>
%H A218750 <a href="/index/Q#q-numbers">Index entries related to q-numbers</a>
%H A218750 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (48,-47)
%F A218750 a(n) = floor(47^n/46).
%F A218750 G.f.: x/(47*x^2-48*x+1) = x/((1-x)*(1-47*x)). [_Colin Barker_, Nov 06 2012]
%F A218750 a(0)=0, a(n) = 47*a(n-1) + 1. - _Vincenzo Librandi_, Nov 08 2012
%F A218750 a(n) = 48*a(n-1) - 47*a(n-2). - _Wesley Ivan Hurt_, Jan 25 2022
%F A218750 E.g.f.: exp(24*x)*sinh(23*x)/23. - _Elmo R. Oliveira_, Aug 27 2024
%t A218750 Table[(47^n - 1)/46, {n, 0, 19}] (* _Alonso del Arte_, Nov 04 2012 *)
%t A218750 LinearRecurrence[{48, -47}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 08 2012 *)
%o A218750 (PARI) A218750(n)=47^n\46
%o A218750 (Maxima) A218750(n):=(47^n-1)/46$ makelist(A218750(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%o A218750 (Magma) [n le 2 select n-1 else 48*Self(n-1) - 47*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 08 2012
%Y A218750 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 A218750 Cf. A009991.
%K A218750 nonn,easy
%O A218750 0,3
%A A218750 _M. F. Hasler_, Nov 04 2012