A016197 - OEIS

%I #23 Jun 29 2023 15:33:23

%S 0,1,23,397,6095,87781,1214423,16344637,215622815,2801832661,

%T 35979939623,457696700077,5777672071535,72470493235141,

%U 904168630965623,11229773405170717,138934529031464255,1713164078241143221

%N a(n) = 12^n - 11^n.

%H Vincenzo Librandi, <a href="/A016197/b016197.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (23, -132).

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

%F E.g.f.: e^(12*x)-e^(11*x). - _Mohammad K. Azarian_, Jan 14 2009

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

%F a(0)=0, a(1)=1, a(n)=23*a(n-1)-132*a(n-2). - _Vincenzo Librandi_, Feb 09 2011

%t f[n_]:= 12^n - 11^n; f[Range[0, 40]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 14 2011 *)

%t CoefficientList[Series[x/((1 - 11 x) (1 - 12 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 03 2014 *)

%o (Magma) [12^n-11^n: n in [0..40]]; // _Vincenzo Librandi_, Aug 03 2014

%o (PARI) a(n)=12^n-11^n \\ _Charles R Greathouse IV_, Aug 03 2014

%Y 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).

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_