OFFSET
0,3
COMMENTS
Partial sums of powers of 29 (A009973).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..600
Index entries for linear recurrences with constant coefficients, signature (30,-29).
FORMULA
a(n) = floor(29^n/28).
G.f.: x/((1-x)*(1-29*x)). - Vincenzo Librandi, Nov 07 2012
a(n) = 30*a(n-1) - 29*a(n-2). - Vincenzo Librandi, Nov 07 2012
E.g.f.: exp(15*x)*sinh(14*x)/14. - Elmo R. Oliveira, Aug 27 2024
MATHEMATICA
LinearRecurrence[{30, -29}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
PROG
(PARI) a(n)=29^n\28
(Magma) [n le 2 select n-1 else 30*Self(n-1)-29*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
(Maxima) A218732(n):=(29^n-1)/28$
makelist(A218732(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.
Cf. A009973.
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved