OFFSET
0,3
COMMENTS
Partial sums of powers of 42 (A009986).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..600
Index entries for linear recurrences with constant coefficients, signature (43,-42).
FORMULA
From Vincenzo Librandi, Nov 07 2012: (Start)
G.f.: x/((1-x)*(1-42*x)).
a(n) = 43*a(n-1) - 42*a(n-2).
a(n) = floor(42^n/41). (End)
E.g.f.: exp(x)*(exp(41*x) - 1)/41. - Elmo R. Oliveira, Aug 29 2024
MATHEMATICA
LinearRecurrence[{43, -42}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
(42^Range[0, 20]-1)/41 (* Harvey P. Dale, May 08 2024 *)
PROG
(PARI) A218745(n)=42^n\41
(Magma) [n le 2 select n-1 else 43*Self(n-1) - 42*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
(Maxima) A218745(n):=(42^n-1)/41$
makelist(A218745(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. A009986.
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved