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A218753 a(n) = (49^n - 1)/48.

%I A218753 #28 Aug 27 2024 18:14:13
%S A218753 0,1,50,2451,120100,5884901,288360150,14129647351,692352720200,
%T A218753 33925283289801,1662338881200250,81454605178812251,
%U A218753 3991275653761800300,195572507034328214701,9583052844682082520350,469569589389422043497151,23008909880081680131360400
%N A218753 a(n) = (49^n - 1)/48.
%C A218753 Partial sums of powers of 49 (A087752).
%H A218753 Vincenzo Librandi, <a href="/A218753/b218753.txt">Table of n, a(n) for n = 0..600</a>
%H A218753 <a href="/index/Par#partial">Index entries related to partial sums</a>
%H A218753 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (50,-49)
%F A218753 G.f.: x/((1-x)*(1-49*x)). - _Vincenzo Librandi_, Nov 08 2012
%F A218753 a(n) = 50*a(n-1) - 49*a(n-2) with a(0)=0, a(1)=1. - _Vincenzo Librandi_, Nov 08 2012
%F A218753 a(n) = 49*a(n-1) + 1 with a(0)=0. - _Vincenzo Librandi_, Nov 08 2012
%F A218753 a(n) = floor(49^n/48). - _Vincenzo Librandi_, Nov 08 2012
%F A218753 E.g.f.: exp(25*x)*sinh(24*x)/24. - _Elmo R. Oliveira_, Aug 27 2024
%t A218753 LinearRecurrence[{50, -49}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 08 2012 *)
%t A218753 Join[{0},Accumulate[49^Range[0,20]]] (* _Harvey P. Dale_, Apr 14 2023 *)
%o A218753 (PARI) A218753(n)=49^n\48
%o A218753 (Maxima) A218753(n):=floor(49^n/48)$ makelist(A218753(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */
%o A218753 (Magma) [n le 2 select n-1 else 50*Self(n-1) - 49*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 08 2012
%Y A218753 Cf. A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218752, A133853, A094028, A218723.
%Y A218753 Cf. A087752.
%K A218753 nonn,easy
%O A218753 0,3
%A A218753 _M. F. Hasler_, Nov 04 2012