A135160 a(n) = 5^n + 3^n - 2^n.

1, 6, 30, 144, 690, 3336, 16290, 80184, 396930, 1972296, 9823650, 49003224, 244667970, 1222289256, 6108282210, 30531894264, 152630871810, 763068462216, 3815084423970, 19074648065304, 95370917376450, 476847616459176, 2384217167880930, 11921023089868344, 59604927188149890, 298024071132008136

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-31,30).

Formula

a(n) = 5^n + 3^n - 2^n.

From Mohammad K. Azarian, Jan 16 2009: (Start)

G.f.: 1/(1-5*x) + 1/(1-3*x) - 1/(1-2*x).

E.g.f.: e^(5*x) + e^(3*x) - e^(2*x). (End)

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

Example

a(4)=690 because 5^4=625, 3^4=81, 2^4=16 and we can write 625 + 81 - 16 = 690.

Mathematica

lst={}; Do[p=5^n+3^n-2^n; AppendTo[lst, p], {n, 0, 7^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 19 2008 *)
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 *)

Prog

(Magma)[5^n+3^n-2^n: n in [0..50]] // Vincenzo Librandi, Dec 15 2010
(PARI) a(n)=5^n+3^n-2^n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A000079, A000244, A000351, A001047.

Sequence in context: A030192 A026376 A026899 * A276022 A046945 A216045

Adjacent sequences: A135157 A135158 A135159 * A135161 A135162 A135163

Keyword

easy,nonn

Author

Omar E. Pol, Nov 21 2007

Extensions

More terms from Vincenzo Librandi, Dec 15 2010

Status

approved