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A218752
a(n) = (50^n - 1)/49.
6
0, 1, 51, 2551, 127551, 6377551, 318877551, 15943877551, 797193877551, 39859693877551, 1992984693877551, 99649234693877551, 4982461734693877551, 249123086734693877551, 12456154336734693877551, 622807716836734693877551, 31140385841836734693877551
OFFSET
0,3
COMMENTS
Partial sums of powers of 50 (A165800).
Converges in a 10-adic sense to ...734693877551.
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
MATHEMATICA
LinearRecurrence[{51, -50}, {0, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *)
(50^Range[0, 20]-1)/49 (* Harvey P. Dale, Sep 12 2022 *)
PROG
(PARI) a(n)=50^n\49
(Maxima) makelist(floor(50^n/49), n, 0, 30); /* Martin Ettl, Nov 06 2012 */;
(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
CROSSREFS
Cf. similar sequences of the form (k^n-1)/(k-1) listed in A269025.
Cf. A165800.
Sequence in context: A231660 A210177 A210080 * A097836 A267786 A267733
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved