A164285 a(n) = 7*2^n + 3.

10, 17, 31, 59, 115, 227, 451, 899, 1795, 3587, 7171, 14339, 28675, 57347, 114691, 229379, 458755, 917507, 1835011, 3670019, 7340035, 14680067, 29360131, 58720259, 117440515, 234881027, 469762051, 939524099, 1879048195, 3758096387

Offset: 0

Author

Vincenzo Librandi, Aug 12 2009

Keywords

• nonn
• easy

Comments

Contains the primes 17, 31, 59, 227, 57347, 114691, 14680067, 7516192771,..

Examples

			At n=0, a(0)=7*2^0+3=10. At n=1, a(1)=7*2^1+3=17.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Programs

Magma

[7*2^n+3: n in [0..40]]; // Vincenzo Librandi, Sep 12 2013

Mathematica

CoefficientList[Series[(10 - 13 x) / ((2 x - 1) (x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 12 2013 *)
LinearRecurrence[{3,-2},{10,17},40] (* Harvey P. Dale, Aug 29 2017 *)

PARI

x='x+O('x^50); Vec((10-13*x)/((2*x-1)*(x-1))) \\ G. C. Greubel, Sep 12 2017

Formula

a(n) = 2*a(n-1) - 3.

a(n) = 3*a(n-1) - 2*a(n-2).

a(n) = A005009(n) + 3, a(0)=10.

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

E.g.f.: 7*exp(2*x) + 3*exp(x). - G. C. Greubel, Sep 12 2017

Extensions

Offset corrected by R. J. Mathar, Aug 19 2009