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A245806 3^n + 10^n. 1

%I

%S 2,13,109,1027,10081,100243,1000729,10002187,100006561,1000019683,

%T 10000059049,100000177147,1000000531441,10000001594323,

%U 100000004782969,1000000014348907,10000000043046721,100000000129140163,1000000000387420489,10000000001162261467

%N 3^n + 10^n.

%H Vincenzo Librandi, <a href="/A245806/b245806.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (13,-30).

%F G.f.: (2-13*x)/((1-3*x)(1-10*x)).

%F E.g.f.: e^(3*x) + e^(10*x).

%F a(n) = 13*a(n-1)-30*a(n-2) for n>1.

%F a(n) = A000244(n) + A011557(n). - _Michel Marcus_, Aug 04 2014

%t Table[(3^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 13 x)/((1 - 3 x) (1 - 10 x)), {x, 0, 30}], x]

%o (MAGMA) [3^n+10^n: n in [0..25]]; /* or */ I:=[2,13]; [n le 2 select I[n] else 13*Self(n-1)-30*Self(n-2): n in [1..25]]

%o (PARI) a(n)=3^n + 10^n \\ _Charles R Greathouse IV_, Aug 26 2014

%Y Cf. 3^n+k^n: A034472 (k=1), A007689 (k=2), A008776 (k=3), A074605 (k=4), A074606 (k=5), A074607 (k=6), A074608 (k=7), A074609 (k=8), A074610 (k=9), this sequence (k=10).

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Aug 04 2014

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Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)