A140360 Inverse binomial transform of A140359.

1, 0, 5, -5, 15, -25, 55, -105, 215, -425, 855, -1705, 3415, -6825, 13655, -27305, 54615, -109225, 218455, -436905, 873815, -1747625, 3495255, -6990505, 13981015, -27962025, 55924055, -111848105, 223696215, -447392425, 894784855, -1789569705, 3579139415

Offset: 0

Author

Paul Curtz, Jun 24 2008

Keywords

• sign

Comments

For p*Jacobsthal numbers A001045, p=2: A078008 (A001045 differences, they are companions) or 1, 2*A001045(n), also in A133494; p=3: A062510; p=4: see A097073; p=6: A092297.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1, 2).

Programs

Maple

a:= n-> `if`(n=0, 1, (<<0|1>, <2|-1>>^(n-1). <<0,5>>)[1,1]):
seq(a(n), n=0..30);  # Alois P. Heinz, Dec 28 2010

Mathematica

{1}~Join~Table[(-5 (-1 + (-2)^(n - 1)))/3, {n, 32}] (* or *)
CoefficientList[Series[(-3 x^2 - x - 1)/(2 x^2 - x - 1), {x, 0, 32}], x] (* Michael De Vlieger, Apr 15 2016 *)

Formula

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

a(n) = (-5*(-1 + (-2)^(n-1)))/3, for n>0. - Andres Cicuttin, Apr 15 2016

a(n) = 5 - 2*a(n-1), for n>2. - Andres Cicuttin, Apr 15 2016

Extensions

More terms from Alois P. Heinz, Dec 28 2010