A218730 a(n) = (27^n - 1)/26.

0, 1, 28, 757, 20440, 551881, 14900788, 402321277, 10862674480, 293292210961, 7918889695948, 213810021790597, 5772870588346120, 155867505885345241, 4208422658904321508, 113627411790416680717, 3067940118341250379360, 82834383195213760242721, 2236528346270771526553468

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 27 (A009971); q-integers for q=27.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..700
• Index entries related to partial sums
• Index entries for linear recurrences with constant coefficients, signature (28,-27).

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. A009971.

Programs

Magma

[n le 2 select n-1 else 28*Self(n-1)-27*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{28, -27}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218730(n):=(27^n-1)/26$
makelist(A218730(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

a(n)=27^n\26

Formula

G.f.: x/((1-x)*(1-27*x)). - Vincenzo Librandi, Nov 07 2012

a(n) = floor(27^n/26). - Vincenzo Librandi, Nov 07 2012

a(n) = 28*a(n-1) - 27*a(n-2). - Vincenzo Librandi, Nov 07 2012

E.g.f.: exp(14*x)*sinh(13*x)/13. - Elmo R. Oliveira, Aug 27 2024