A218750 a(n) = (47^n - 1)/46.

0, 1, 48, 2257, 106080, 4985761, 234330768, 11013546097, 517636666560, 24328923328321, 1143459396431088, 53742591632261137, 2525901806716273440, 118717384915664851681, 5579717091036248029008, 262246703278703657363377, 12325595054099071896078720

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 47 (A009991).

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 (48,-47)

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. A009991.

Programs

Magma

[n le 2 select n-1 else 48*Self(n-1) - 47*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 08 2012

Mathematica

Table[(47^n - 1)/46, {n, 0, 19}] (* Alonso del Arte, Nov 04 2012 *)
LinearRecurrence[{48, -47}, {0, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *)

Maxima

A218750(n):=(47^n-1)/46$ makelist(A218750(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218750(n)=47^n\46

Formula

a(n) = floor(47^n/46).

G.f.: x/(47*x^2-48*x+1) = x/((1-x)*(1-47*x)). [Colin Barker, Nov 06 2012]

a(0)=0, a(n) = 47*a(n-1) + 1. - Vincenzo Librandi, Nov 08 2012

a(n) = 48*a(n-1) - 47*a(n-2). - Wesley Ivan Hurt, Jan 25 2022

E.g.f.: exp(24*x)*sinh(23*x)/23. - Elmo R. Oliveira, Aug 27 2024