A218727 a(n) = (24^n - 1)/23.

0, 1, 25, 601, 14425, 346201, 8308825, 199411801, 4785883225, 114861197401, 2756668737625, 66160049703001, 1587841192872025, 38108188628928601, 914596527094286425, 21950316650262874201, 526807599606308980825, 12643382390551415539801, 303441177373233972955225

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 24 (A009968); q-integers for q=24: diagonal k=1 in triangle A022188.

Partial sums are in A014913. Also, the sequence is related to A014942 by A014942(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 (25,-24).

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. A009968, A014942, A022188.

Programs

Magma

[n le 2 select n-1 else 25*Self(n-1)-24*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{25, -24}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218727(n):=(24^n-1)/23$
makelist(A218727(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218727(n)=24^n\23

Formula

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1-x)*(1-24*x)).

a(n) = floor(24^n/23).

a(n) = 25*a(n-1) - 24*a(n-2). (End)

E.g.f.: exp(x)*(exp(23*x) - 1)/23. - Elmo R. Oliveira, Aug 29 2024