A218745 a(n) = (42^n - 1)/41.

0, 1, 43, 1807, 75895, 3187591, 133878823, 5622910567, 236162243815, 9918814240231, 416590198089703, 17496788319767527, 734865109430236135, 30864334596069917671, 1296302053034936542183, 54444686227467334771687, 2286676821553628060410855, 96040426505252378537255911

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 42 (A009986).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..600
• Index entries related to partial sums.
• Index entries related to q-numbers.
• Index entries for linear recurrences with constant coefficients, signature (43,-42).

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.

Programs

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

Mathematica

LinearRecurrence[{43, -42}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
(42^Range[0,20]-1)/41 (* Harvey P. Dale, May 08 2024 *)

Maxima

A218745(n):=(42^n-1)/41$
makelist(A218745(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218745(n)=42^n\41

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