A218732 a(n) = (29^n - 1)/28.

0, 1, 30, 871, 25260, 732541, 21243690, 616067011, 17865943320, 518112356281, 15025258332150, 435732491632351, 12636242257338180, 366451025462807221, 10627079738421409410, 308185312414220872891, 8937374060012405313840, 259183847740359754101361

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 29 (A009973).

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 (30,-29).

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. A009973.

Programs

Magma

[n le 2 select n-1 else 30*Self(n-1)-29*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{30, -29}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218732(n):=(29^n-1)/28$
makelist(A218732(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

a(n)=29^n\28

Formula

a(n) = floor(29^n/28).

G.f.: x/((1-x)*(1-29*x)). - Vincenzo Librandi, Nov 07 2012

a(n) = 30*a(n-1) - 29*a(n-2). - Vincenzo Librandi, Nov 07 2012

E.g.f.: exp(15*x)*sinh(14*x)/14. - Elmo R. Oliveira, Aug 27 2024