A218733 a(n) = (30^n - 1)/29.

0, 1, 31, 931, 27931, 837931, 25137931, 754137931, 22624137931, 678724137931, 20361724137931, 610851724137931, 18325551724137931, 549766551724137931, 16492996551724137931, 494789896551724137931, 14843696896551724137931, 445310906896551724137931, 13359327206896551724137931

Offset

0,3

Comments

Partial sums of powers of 30 (A009974).

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 (31,-30).

Formula

a(n) = floor(30^n/29).

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1-x)*(1-30*x)).

a(n) = 31*a(n-1) - 30*a(n-2). (End)

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

Mathematica

LinearRecurrence[{31, -30}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
(30^Range[0, 20]-1)/29 (* Harvey P. Dale, Nov 22 2022 *)

Prog

(PARI) A218733(n)=30^n\29
(Maxima) A218733(n):=floor((30^n-1)/29)$ makelist(A218733(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(Magma) [n le 2 select n-1 else 31*Self(n-1) - 30*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Crossrefs

Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.

Cf. A009974.

Sequence in context: A170664 A170712 A170750 * A084330 A238993 A171336

Adjacent sequences: A218730 A218731 A218732 * A218734 A218735 A218736

Keyword

nonn,easy

Author

M. F. Hasler, Nov 04 2012

Status

approved