A218738 a(n) = (35^n - 1)/34.

0, 1, 36, 1261, 44136, 1544761, 54066636, 1892332261, 66231629136, 2318107019761, 81133745691636, 2839681099207261, 99388838472254136, 3478609346528894761, 121751327128511316636, 4261296449497896082261, 149145375732426362879136, 5220088150634922700769761

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 35 (A009979).

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 (36,-35).

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. A009979.

Programs

Magma

[n le 2 select n-1 else 36*Self(n-1)-35*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{36, -35}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218738(n):=(35^n-1)/34$
makelist(A218738(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218738(n)=35^n\34

Formula

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1 - x)*(1 - 35*x)).

a(n) = 36*a(n-1) - 35*a(n-2).

a(n) = floor(35^n/34). (End)

E.g.f.: exp(x)*(exp(34*x) - 1)/34. - Stefano Spezia, Mar 28 2023