A373568 Expansion of x - 1/(x - 1/(x - 1/(x - 1/(x + 1)))).

1, 5, 10, 30, 85, 246, 707, 2037, 5864, 16886, 48620, 139997, 403104, 1160693, 3342081, 9623140, 27708726, 79784098, 229729153, 661478734, 1904652103, 5484227157, 15791202736, 45468956106, 130922641160, 376976720745, 1085461206128, 3125460977225, 8999406210929

Offset: 0

Author

Peter Luschny, Jun 10 2024

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,3,-1,-1).

Crossrefs

Essentially the same as A006357.

Programs

Mathematica

CoefficientList[Series[x - 1/(x - 1/(x - 1/(x - 1/(x + 1)))), {x, 0, 28}], x] (* Michael De Vlieger, Jun 10 2024 *)

Formula

a(n) = [x^n] (x^5 + x^4 - 4*x^3 - 3*x^2 + 3*x + 1)/(x^4 + x^3 - 3*x^2 - 2*x + 1).