A218746 a(n) = (43^n - 1)/42.

0, 1, 44, 1893, 81400, 3500201, 150508644, 6471871693, 278290482800, 11966490760401, 514559102697244, 22126041415981493, 951419780887204200, 40911050578149780601, 1759175174860440565844, 75644532518998944331293, 3252714898316954606245600, 139866740627629048068560801

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 43 (A009987).

0 followed by the binomial transform of A170762. - R. J. Mathar, Jul 18 2015

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 (44,-43)

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. A009987, A170762.

Programs

Magma

[n le 2 select n-1 else 44*Self(n-1) - 43*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{44, -43}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
Join[{0},Accumulate[43^Range[0,20]]] (* Harvey P. Dale, Jan 27 2015 *)

Maxima

A218746(n):=(43^n-1)/42$
makelist(A218746(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218746(n)=43^n\42

Formula

G.f.: x/((1-x)*(1-43*x)). - Vincenzo Librandi, Nov 07 2012

a(n) = 44*a(n-1) - 43*a(n-2). - Vincenzo Librandi, Nov 07 2012

a(n) = floor(43^n/42). - Vincenzo Librandi, Nov 07 2012

E.g.f.: exp(22*x)*sinh(21*x)/21. - Elmo R. Oliveira, Aug 27 2024