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a(n) = (50^n - 1)/49.
6

%I #36 Aug 29 2024 15:59:42

%S 0,1,51,2551,127551,6377551,318877551,15943877551,797193877551,

%T 39859693877551,1992984693877551,99649234693877551,

%U 4982461734693877551,249123086734693877551,12456154336734693877551,622807716836734693877551,31140385841836734693877551

%N a(n) = (50^n - 1)/49.

%C Partial sums of powers of 50 (A165800).

%C Converges in a 10-adic sense to ...734693877551.

%H Vincenzo Librandi, <a href="/A218752/b218752.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 (51,-50).

%F a(n) = floor(50^n/49).

%F G.f.: x/((1-x)(1-50x)).

%F a(0)=0, a(n) = 50*a(n-1) + 1. - _Vincenzo Librandi_, Nov 08 2012

%F E.g.f.: exp(x)*(exp(49*x) - 1)/49. - _Elmo R. Oliveira_, Aug 29 2024

%t LinearRecurrence[{51, -50}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 08 2012 *)

%t (50^Range[0,20]-1)/49 (* _Harvey P. Dale_, Sep 12 2022 *)

%o (PARI) a(n)=50^n\49

%o (Maxima) makelist(floor(50^n/49), n, 0, 30); /* _Martin Ettl_, Nov 06 2012 */;

%o (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 Cf. similar sequences of the form (k^n-1)/(k-1) listed in A269025.

%Y Cf. A165800.

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, Nov 04 2012