A218726 a(n) = (23^n - 1)/22.

0, 1, 24, 553, 12720, 292561, 6728904, 154764793, 3559590240, 81870575521, 1883023236984, 43309534450633, 996119292364560, 22910743724384881, 526947105660852264, 12119783430199602073, 278755018894590847680, 6411365434575589496641, 147461404995238558422744

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 23, q-integers for q=23: diagonal k=1 in triangle A022187.

Partial sums are in A014909. Also, the sequence is related to A014941 by A014941(n) = n*a(n) - Sum{a(i), i=0..n-1} 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 (24,-23).

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. A014909, A014941, A022187.

Programs

Magma

[n le 2 select n-1 else 24*Self(n-1)-23*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{24, -23}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
(23^Range[0,20]-1)/22 (* Harvey P. Dale, Nov 09 2012 *)

Maxima

A218726(n):=(23^n-1)/22$
makelist(A218726(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218726(n)=23^n\22

Formula

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1-x)*(1-23*x)).

a(n) = floor(23^n/22).

a(n) = 24*a(n-1) - 23*a(n-2). (End)

E.g.f.: exp(12*x)*sinh(11*x)/11. - Elmo R. Oliveira, Aug 27 2024