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%I #23 Oct 05 2024 16:30:28
%S 1,4,52,658,7600,83194,882352,9176458,94235200,959646394,9717524752,
%T 98022673258,986158712800,9903110989594,99321776927152,
%U 995252438490058,9966767069430400,99767369486012794,998371586402089552
%N a(n) = 10^n - 7^n + 1.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-87,70).
%F G.f.: 1/(1-10*x)-1/(1-7*x)+1/(1-x).
%F E.g.f.: e^(10*x)-e^(7*x)+e^x.
%F a(n) = 17*a(n-1)-70*a(n-2)+54 with a(0)=1, a(1)=4. - _Vincenzo Librandi_, Jul 21 2010
%F a(0)=1, a(1)=4, a(2)=52, a(n)=18*a(n-1)-87*a(n-2)+70*a(n-3). - _Harvey P. Dale_, May 05 2011
%t Table[10^n-7^n+1,{n,0,20}] (* or *) LinearRecurrence[{18,-87,70},{1,4,52}, 21] (* _Harvey P. Dale_, May 05 2011 *)
%o (PARI) a(n)=10^n-7^n+1 \\ _Charles R Greathouse IV_, Jun 11 2015
%Y Cf. A155638, A155639, A155640, A155641, A155642, A155643, A155644, A155645, A155646, A155647, A155648, A155649, A155650, A155651, A155652, A155653, A155654, A155655, A155656, A155657, A155658, A155659, A155660.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_, Jan 31 2009