OFFSET
0,3
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 for linear recurrences with constant coefficients, signature (26,-25).
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
MATHEMATICA
LinearRecurrence[{26, -25}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
(25^Range[0, 20]-1)/24 (* Harvey P. Dale, Aug 23 2020 *)
PROG
(PARI) A218728(n)=25^n\24
(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
(Maxima) A218728(n):=(25^n-1)/24$
makelist(A218728(n), n, 0, 30); /* Martin Ettl, Nov 07 2012 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved