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7^n+6^n-1.
15

%I #16 Jun 12 2015 15:26:54

%S 1,12,84,558,3696,24582,164304,1103478,7444416,50431302,342941424,

%T 2340123798,16018069536,109949704422,756587236944,5217746494518,

%U 36054040477056,249557173431942,1729973554578864,12008254925383638

%N 7^n+6^n-1.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (14,-55,42).

%F G.f.: 1/(1-7*x)+1/(1-6*x)-1/(1-x). E.g.f.: e^(7*x)+e^(6*x)-e^x.

%F a(n)=13*a(n-1)-42*a(n-2)-30 with a(0)=1, a(1)=12 - _Vincenzo Librandi_, Jul 21 2010

%F a(0)=1, a(1)=12, a(2)=84, a(n)=14*a(n-1)-55*a(n-2)+42*a(n-3) [From Harvey P. Dale, May 08 2012]

%t Table[7^n+6^n-1,{n,0,20}] (* or *) LinearRecurrence[{14,-55,42},{1,12,84},20] (* _Harvey P. Dale_, May 08 2012 *)

%o (PARI) a(n)=7^n+6^n-1 \\ _Charles R Greathouse IV_, Jun 11 2015

%Y Cf. A155628, A155629, A155630, A155631, A155632, A155633, A155634, A155635, A155636, A155637, A155638, A155639, A155640, A155641, A155642, A155643, A155644.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Jan 31 2009