A155596 - OEIS

%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