A218729 a(n) = (26^n - 1)/25.

0, 1, 27, 703, 18279, 475255, 12356631, 321272407, 8353082583, 217180147159, 5646683826135, 146813779479511, 3817158266467287, 99246114928149463, 2580398988131886039, 67090373691429037015, 1744349715977154962391, 45353092615406029022167, 1179180408000556754576343

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 26 (A009970); q-integers for q=26.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..700
• Index entries related to partial sums.
• Index entries for linear recurrences with constant coefficients, signature (27,-26).

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. A009970.

Programs

Magma

[n le 2 select n-1 else 27*Self(n-1)-26*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{27, -26}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218729(n):=(26^n-1)/25$
makelist(A218729(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218729(n)=26^n\25

Formula

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1-x)*(1-26*x)).

a(n) = floor(26^n/25).

a(n) = 27*a(n-1) - 26*a(n-2). (End)

E.g.f.: exp(x)*(exp(25*x) - 1)/25. - Elmo R. Oliveira, Aug 29 2024