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%I #29 Sep 08 2022 08:45:32
%S 1,6,30,144,690,3336,16290,80184,396930,1972296,9823650,49003224,
%T 244667970,1222289256,6108282210,30531894264,152630871810,
%U 763068462216,3815084423970,19074648065304,95370917376450,476847616459176,2384217167880930,11921023089868344,59604927188149890,298024071132008136
%N a(n) = 5^n + 3^n - 2^n.
%H G. C. Greubel, <a href="/A135160/b135160.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-31,30).
%F a(n) = 5^n + 3^n - 2^n.
%F From _Mohammad K. Azarian_, Jan 16 2009: (Start)
%F G.f.: 1/(1-5*x) + 1/(1-3*x) - 1/(1-2*x).
%F E.g.f.: e^(5*x) + e^(3*x) - e^(2*x). (End)
%F a(0)=1, a(1)=6, a(2)=30, a(n) = 10*a(n-1) - 31*a(n-2) + 30*a(n-3). - _Harvey P. Dale_, Mar 10 2013
%e a(4)=690 because 5^4=625, 3^4=81, 2^4=16 and we can write 625 + 81 - 16 = 690.
%t lst={};Do[p=5^n+3^n-2^n;AppendTo[lst, p], {n, 0, 7^2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 19 2008 *)
%t Table[5^n+3^n-2^n,{n,0,30}] (* or *) LinearRecurrence[{10,-31,30},{1,6,30},30] (* _Harvey P. Dale_, Mar 10 2013 *)
%o (Magma)[5^n+3^n-2^n: n in [0..50]] // _Vincenzo Librandi_, Dec 15 2010
%o (PARI) a(n)=5^n+3^n-2^n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A000079, A000244, A000351, A001047.
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, Nov 21 2007
%E More terms from _Vincenzo Librandi_, Dec 15 2010
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