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%I #26 Mar 10 2022 05:29:35
%S 1,4,22,118,610,3094,15562,77998,390370,1952614,9764602,48826078,
%T 244136530,1220694934,6103499242,30517545358,152587825090,
%U 762939322054,3814697003482,19073485803838,95367430592050,476837156105974
%N a(n) = 5^n - 2^n + 1^n.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-17,10).
%F G.f.: 1/(1-5*x)-1/(1-2*x)+1/(1-x).
%F E.g.f.: e^(5*x) - e^(2*x) + e^x.
%F a(n) = 7*a(n-1)-10*a(n-2)+4 with a(0)=1, a(1)=4. - _Vincenzo Librandi_, Jul 21 2010
%F a(n) = A005057(n)+1. - _R. J. Mathar_, Mar 10 2022
%t Table[5^n-2^n+1,{n,0,30}] (* or *) LinearRecurrence[{8,-17,10},{1,4,22},30] (* _Harvey P. Dale_, Sep 11 2019 *)
%o (PARI) a(n)=5^n-2^n+1 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_, Jan 25 2009
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