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A218726 a(n) = (23^n-1)/22. 4
0, 1, 24, 553, 12720, 292561, 6728904, 154764793, 3559590240, 81870575521, 1883023236984, 43309534450633, 996119292364560, 22910743724384881, 526947105660852264, 12119783430199602073, 278755018894590847680, 6411365434575589496641 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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).

FORMULA

G.f.: x/((1-x)*(1-23*x)). - Vincenzo Librandi, Nov 07 2012

a(n) = floor(23^n/22). - Vincenzo Librandi, Nov 07 2012

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

PROG

(PARI) A218726(n)=23^n\22

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

(Maxima) A218726(n):=(23^n-1)/22$

makelist(A218726(n), n, 0, 30); /* Martin Ettl, Nov 07 2012 */

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.

Sequence in context: A170657 A170705 A170743 * A203487 A007110 A007109

Adjacent sequences:  A218723 A218724 A218725 * A218727 A218728 A218729

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Nov 04 2012

STATUS

approved

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Last modified June 18 15:13 EDT 2019. Contains 324213 sequences. (Running on oeis4.)