A165746 a(n) = 3 - 2*3^n.

1, -3, -15, -51, -159, -483, -1455, -4371, -13119, -39363, -118095, -354291, -1062879, -3188643, -9565935, -28697811, -86093439, -258280323, -774840975, -2324522931, -6973568799, -20920706403, -62762119215, -188286357651

Offset: 0

Author

Philippe Deléham, Sep 26 2009

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A008776, A112555.

Programs

Magma

[3-2*3^n : n in [0..30]]; // Vincenzo Librandi, Nov 03 2011

Mathematica

Table[3-2*3^n,{n,0,30}] (* or *) LinearRecurrence[{4,-3},{1,-3},30] (* Harvey P. Dale, Aug 29 2024 *)

Formula

G.f.: (1-7*x)/(1 - 4*x + 3*x^2).

a(n) = 3 - A008776(n).

a(n) = 4*a(n-1) - 3*a(n-2) for n > 1; a(0)=1, a(1)=-3.

a(n) = Sum_{k=0..n} A112555(n,k)*(-4)^(n-k).

a(n) = 3*a(n-1) - 6. - Vincenzo Librandi, Nov 03 2011