A218725 a(n) = (22^n - 1)/21.

0, 1, 23, 507, 11155, 245411, 5399043, 118778947, 2613136835, 57489010371, 1264758228163, 27824681019587, 612142982430915, 13467145613480131, 296277203496562883, 6518098476924383427, 143398166492336435395, 3154759662831401578691, 69404712582290834731203

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 22; q-integers for q=22: Diagonal k=1 in the triangle A022186.

Partial sums are in A014907. Also, the sequence is related to A014940 by A014940(n) = n*a(n) - Sum_{i=0..n-1} a(i) for n > 0. [Bruno Berselli, Nov 06 2012]

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 (23,-22).

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. A014907, A014940, A022186.

Programs

Magma

[n le 2 select n-1 else 23*Self(n-1) - 22*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{23, -22}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218725(n):=(22^n-1)/21$ makelist(A218725(n),n,0,30); /* Martin Ettl, Nov 06 2012 */

PARI

A218725(n)=22^n\21

Formula

a(n) = floor(22^n/21).

G.f.: x/((1-x)*(1-22*x)). [Bruno Berselli, Nov 06 2012]

a(n) = 23*a(n-1) - 22*a(n-2). - Vincenzo Librandi, Nov 07 2012

E.g.f.: exp(x)*(exp(21*x) - 1)/21. - Elmo R. Oliveira, Aug 29 2024