A218728 a(n) = (25^n - 1)/24.

0, 1, 26, 651, 16276, 406901, 10172526, 254313151, 6357828776, 158945719401, 3973642985026, 99341074625651, 2483526865641276, 62088171641031901, 1552204291025797526, 38805107275644938151, 970127681891123453776, 24253192047278086344401, 606329801181952158610026

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 25 (A009969); q-integers for q=25.

Partial sums are in A014914. Also, the sequence is related to A014943 by A014943(n) = n*a(n) - Sum_{i=0..n-1} a(i) for n > 0. - Bruno Berselli, Nov 07 2012

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 (26,-25).

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. A009969, A014914, A014943.

Programs

Magma

[n le 2 select n-1 else 26*Self(n-1)-25*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{26, -25}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
(25^Range[0,20]-1)/24 (* Harvey P. Dale, Aug 23 2020 *)

Maxima

A218728(n):=(25^n-1)/24$
makelist(A218728(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218728(n)=25^n\24

Formula

a(n) = floor(25^n/24).

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1-x)*(1-25*x)).

a(n) = 26*a(n-1) - 25*a(n-2). (End)

E.g.f.: exp(13*x)*sinh(12*x)/12. - Elmo R. Oliveira, Aug 27 2024