A016197 a(n) = 12^n - 11^n.

0, 1, 23, 397, 6095, 87781, 1214423, 16344637, 215622815, 2801832661, 35979939623, 457696700077, 5777672071535, 72470493235141, 904168630965623, 11229773405170717, 138934529031464255, 1713164078241143221

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (23, -132).

Crossrefs

Cf. k^n-(k-1)^n: A000225 (k=2), A001047 (k=3), A005061 (k=4), A005060 (k=5), A005062 (k=6), A016169 (k=7), A016177 (k=8), A016185 (k=9), A016189 (k=10), A016195 (k=11), this sequence (k=12).

Programs

Magma

[12^n-11^n: n in [0..40]]; // Vincenzo Librandi, Aug 03 2014

Mathematica

f[n_]:= 12^n - 11^n; f[Range[0, 40]] (* Vladimir Joseph Stephan Orlovsky, Feb 14 2011 *)
CoefficientList[Series[x/((1 - 11 x) (1 - 12 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 03 2014 *)

PARI

a(n)=12^n-11^n \\ Charles R Greathouse IV, Aug 03 2014

Formula

G.f.: x/((1-11x)(1-12x)).

E.g.f.: e^(12*x)-e^(11*x). - Mohammad K. Azarian, Jan 14 2009

a(0)=0, a(n)=12*a(n-1)+11^(n-1). - _Vincenzo Librandi-, Feb 09 2011

a(0)=0, a(1)=1, a(n)=23*a(n-1)-132*a(n-2). - Vincenzo Librandi, Feb 09 2011