A383953 a(0) = 4, a(n) = 2*a(n-1) + (-1)^n.

4, 7, 15, 29, 59, 117, 235, 469, 939, 1877, 3755, 7509, 15019, 30037, 60075, 120149, 240299, 480597, 961195, 1922389, 3844779, 7689557, 15379115, 30758229, 61516459, 123032917, 246065835, 492131669, 984263339, 1968526677, 3937053355, 7874106709, 15748213419, 31496426837

Offset: 0

Author

Paul Curtz, Aug 19 2025

Keywords

• nonn
• easy
• new

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2).

Crossrefs

Cf. A005015, A052997, A340627.

Bisections give A199210 and A072261.

Programs

Mathematica

a[n_] := (11*2^n + (-1)^n)/3; Array[a, 34, 0] (* Amiram Eldar, Aug 20 2025 *)

Formula

a(n) = (11*2^n + (-1)^n)/3.

a(n) = A340627(n+1)/2.

a(n) = 2*A052997(n) + 1 for n >= 1.

a(n) = a(n-4) + 55*2^(n-4) for n >= 4.

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

E.g.f: (11*exp(2*x) + exp(-x))/3.