A245806 a(n) = 3^n + 10^n.

2, 13, 109, 1027, 10081, 100243, 1000729, 10002187, 100006561, 1000019683, 10000059049, 100000177147, 1000000531441, 10000001594323, 100000004782969, 1000000014348907, 10000000043046721, 100000000129140163, 1000000000387420489, 10000000001162261467

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (13,-30).

Formula

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

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

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

a(n) = A000244(n) + A011557(n). - Michel Marcus, Aug 04 2014

Mathematica

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

Prog

(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]]
(PARI) a(n)=3^n + 10^n \\ Charles R Greathouse IV, Aug 26 2014

Crossrefs

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).

Sequence in context: A371581 A264621 A367648 * A192204 A176932 A258916

Adjacent sequences: A245803 A245804 A245805 * A245807 A245808 A245809

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 04 2014

Status

approved