A218748 a(n) = (45^n - 1)/44.

0, 1, 46, 2071, 93196, 4193821, 188721946, 8492487571, 382161940696, 17197287331321, 773877929909446, 34824506845925071, 1567102808066628196, 70519626362998268821, 3173383186334922096946, 142802243385071494362571, 6426100952328217246315696

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 45 (A009989).

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 (46,-45).

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. A009989.

Programs

Magma

[n le 2 select n-1 else 46*Self(n-1) - 45*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 08 2012

Mathematica

LinearRecurrence[{46, -45}, {0, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *)

Maxima

A218748(n):=(45^n-1)/44$ makelist(A218748(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218748(n)=45^n\44

Formula

G.f.: x/((1-x)*(1-45*x)). - Vincenzo Librandi, Nov 08 2012

a(n) = 46*a(n-1) - 45*a(n-2) with a(0)=0, a(1)=1. - Vincenzo Librandi, Nov 08 2012

a(n) = 45*a(n-1) + 1 with a(0)=0. - Vincenzo Librandi, Nov 08 2012

a(n) = floor(45^n/44). - Vincenzo Librandi, Nov 08 2012

E.g.f.: exp(23*x)*sinh(22*x)/22. - Elmo R. Oliveira, Aug 27 2024