A218752 a(n) = (50^n - 1)/49.

0, 1, 51, 2551, 127551, 6377551, 318877551, 15943877551, 797193877551, 39859693877551, 1992984693877551, 99649234693877551, 4982461734693877551, 249123086734693877551, 12456154336734693877551, 622807716836734693877551, 31140385841836734693877551

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 50 (A165800).

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..600
• Index entries related to partial sums.
• Index entries for linear recurrences with constant coefficients, signature (51,-50).

Crossrefs

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

Cf. A165800.

Programs

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

Mathematica

LinearRecurrence[{51, -50}, {0, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *)
(50^Range[0,20]-1)/49 (* Harvey P. Dale, Sep 12 2022 *)

Maxima

makelist(floor(50^n/49), n, 0, 30); /* Martin Ettl, Nov 06 2012 */

PARI

a(n)=50^n\49

Formula

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

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

a(0)=0, a(n) = 50*a(n-1) + 1. - Vincenzo Librandi, Nov 08 2012

E.g.f.: exp(x)*(exp(49*x) - 1)/49. - Elmo R. Oliveira, Aug 29 2024