A165553 a(n) = (3/2)*(1+(-3)^(n-1)).

1, 3, -3, 15, -39, 123, -363, 1095, -3279, 9843, -29523, 88575, -265719, 797163, -2391483, 7174455, -21523359, 64570083, -193710243, 581130735, -1743392199, 5230176603, -15690529803, 47071589415, -141214768239

Offset: 0

Author

Philippe Deléham, Sep 21 2009

Keywords

• easy
• sign

Comments

a(n)/a(n-1) tends to -3.

Links

• Index entries for linear recurrences with constant coefficients, signature (-2,3).

Crossrefs

Cf. A046717, A084247, A112555.

Programs

Mathematica

3/2*(1 + (-3)^(Range[0, 29] - 1)) (* or *)
LinearRecurrence[{-2, 3}, {1, 3}, 30] (* Paolo Xausa, Apr 22 2024 *)

Formula

a(0)=1, a(1)=3, a(n)=3*a(n-2)-2*a(n-1).

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

a(n)= Sum_{k=0..n} A112555(n,k)*2^(n-k).