A218743 a(n) = (40^n - 1)/39.

0, 1, 41, 1641, 65641, 2625641, 105025641, 4201025641, 168041025641, 6721641025641, 268865641025641, 10754625641025641, 430185025641025641, 17207401025641025641, 688296041025641025641, 27531841641025641025641, 1101273665641025641025641, 44050946625641025641025641

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 40 (A009983).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..600
• Index entries related to partial sums.
• Index entries for linear recurrences with constant coefficients, signature (41,-40).

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. A009983.

Programs

Magma

[n le 2 select n-1 else 41*Self(n-1) - 40*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{41, -40}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218743(n):=floor(40^n/39)$ makelist(A218743(n),n,0,30); /* Martin Ettl, Nov 05 2012 */

PARI

a(n)=40^n\39

Formula

a(n) = floor(40^n/39).

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1-x)*(1-40*x)).

a(n) = 41*a(n-1) - 40*a(n-2). (End)

E.g.f.: exp(x)*(exp(39*x) - 1)/39. - Elmo R. Oliveira, Aug 29 2024