A218737 a(n) = (34^n - 1)/33.

0, 1, 35, 1191, 40495, 1376831, 46812255, 1591616671, 54114966815, 1839908871711, 62556901638175, 2126934655697951, 72315778293730335, 2458736461986831391, 83597039707552267295, 2842299350056777088031, 96638177901930420993055, 3285698048665634313763871

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 34 (A009978).

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 (35,-34).

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.

Programs

Magma

[n le 2 select n-1 else 35*Self(n-1)-34*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{35, -34}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218737(n):=(34^n-1)/33$
makelist(A218737(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218737(n)=34^n\33

Formula

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1 - x)*(1 - 34*x)).

a(n) = 35*a(n-1) - 34*a(n-2).

a(n) = floor(34^n/33). (End)

E.g.f.: exp(x)*(exp(33*x) - 1)/33. - Stefano Spezia, Mar 26 2023