This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A218752 #39 Nov 15 2024 18:02:44
%S A218752 0,1,51,2551,127551,6377551,318877551,15943877551,797193877551,
%T A218752 39859693877551,1992984693877551,99649234693877551,
%U A218752 4982461734693877551,249123086734693877551,12456154336734693877551,622807716836734693877551,31140385841836734693877551
%N A218752 a(n) = (50^n - 1)/49.
%C A218752 Partial sums of powers of 50 (A165800).
%C A218752 Converges in a 10-adic sense to ...734693877551.
%H A218752 Vincenzo Librandi, <a href="/A218752/b218752.txt">Table of n, a(n) for n = 0..600</a>
%H A218752 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218752 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (51,-50).
%F A218752 a(n) = floor(50^n/49).
%F A218752 G.f.: x/((1-x)(1-50x)).
%F A218752 a(0)=0, a(n) = 50*a(n-1) + 1. - _Vincenzo Librandi_, Nov 08 2012
%F A218752 E.g.f.: exp(x)*(exp(49*x) - 1)/49. - _Elmo R. Oliveira_, Aug 29 2024
%t A218752 LinearRecurrence[{51, -50}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 08 2012 *)
%t A218752 (50^Range[0,20]-1)/49 (* _Harvey P. Dale_, Sep 12 2022 *)
%o A218752 (PARI) a(n)=50^n\49
%o A218752 (Maxima) makelist(floor(50^n/49), n, 0, 30); /* _Martin Ettl_, Nov 06 2012 */
%o A218752 (Magma) [n le 2 select n-1 else 51*Self(n-1) - 50*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 08 2012
%Y A218752 Cf. similar sequences of the form (k^n-1)/(k-1) listed in A269025.
%Y A218752 Cf. A165800.
%K A218752 nonn,easy
%O A218752 0,3
%A A218752 _M. F. Hasler_, Nov 04 2012