%I #18 Jan 30 2026 17:11:20

%S 1,6,86,1116,13346,153276,1724906,19207236,212679266,2347869996,

%T 25876958426,284948873556,3136251594386,34509651449916,

%U 379671469419146,4176777984431076,45946908753664706,505430101839849036

%N a(n) = 11^n - 6^n + 1.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (18,-83,66).

%F G.f.: 1/(1-11*x)-1/(1-6*x)+1/(1-x). E.g.f.: e^(11*x)-e^(6*x)+e^x.

%F a(n)=17*a(n-1)-66*a(n-2)+50 with a(0)=1, a(1)=6 [From _Vincenzo Librandi_, Jul 21 2010]

%t Table[11^n-6^n+1,{n,0,30}] (* or *) LinearRecurrence[{18,-83,66},{1,6,86},30] (* _Harvey P. Dale_, Apr 11 2023 *)

%o (PARI) a(n)= 11^n-6^n+1 \\ _Charles R Greathouse IV_, Dec 22 2011

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Jan 31 2009