OFFSET
0,3
COMMENTS
Partial sums of powers of 38 (A009982).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..600
Index entries for linear recurrences with constant coefficients, signature (39,-38).
FORMULA
From Vincenzo Librandi, Nov 07 2012: (Start)
G.f.: x/((1-x)*(1-38*x)).
a(n) = 39*a(n-1) - 38*a(n-2).
a(n) = floor(38^n/37). (End)
E.g.f.: exp(x)*(exp(37*x) - 1)/37. - Elmo R. Oliveira, Aug 29 2024
MATHEMATICA
LinearRecurrence[{39, -38}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
PROG
(PARI) A218741(n)=38^n\37
(Magma) [n le 2 select n-1 else 39*Self(n-1) - 38*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
(Maxima) A218741(n):=(38^n-1)/37$
makelist(A218741(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. A009982.
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved