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 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
E.g.f.: exp(12*x)*sinh(11*x)/11. - Elmo R. Oliveira, Aug 27 2024
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
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved