A218744 a(n) = (41^n - 1)/40.

0, 1, 42, 1723, 70644, 2896405, 118752606, 4868856847, 199623130728, 8184548359849, 335566482753810, 13758225792906211, 564087257509154652, 23127577557875340733, 948230679872888970054, 38877457874788447772215, 1593975772866326358660816, 65353006687519380705093457

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 41 (A009985).

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 (42,-41).

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. A009985.

Programs

Magma

[n le 2 select n-1 else 42*Self(n-1)-41*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{42, -41}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218744(n):=(41^n-1)/40$
makelist(A218744(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218744(n)=41^n\40

Formula

a(n) = floor(41^n/40).

G.f.: x/((1-x)*(1-41*x)). - Vincenzo Librandi, Nov 07 2012

a(n) = 42*a(n-1) - 41*a(n-2). - Vincenzo Librandi, Nov 07 2012

E.g.f.: exp(21*x)*sinh(20*x)/20. - Elmo R. Oliveira, Aug 27 2024