A356050 a(n) = 2*A135318(n+1) - A135318(n).

1, 1, 3, 4, 5, 6, 11, 14, 21, 26, 43, 54, 85, 106, 171, 214, 341, 426, 683, 854, 1365, 1706, 2731, 3414, 5461, 6826, 10923, 13654, 21845, 27306, 43691, 54614, 87381, 109226, 174763, 218454, 349525, 436906, 699051, 873814, 1398101, 1747626, 2796203, 3495254, 5592405

Offset: 0

Author

Paul Curtz, Aug 19 2022

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,0,2).

Crossrefs

Cf. A001045, A084214, A135318, A230096.

Cf. A094958.

Programs

Mathematica

LinearRecurrence[{0, 1, 0, 2}, {1, 1, 3, 4}, 50] (* Amiram Eldar, Aug 19 2022 *)

Formula

a(n) = A135318(n) + A230096(n+1).

a(n) = a(n-8) + 5*A094958(n-5).

a(2*n) = A001045(n+2).

a(2*n+1) = A084214(n+1).

From Stefano Spezia, Aug 20 2022: (Start)

O.g.f.: (1 + x + 2*x^2 + 3*x^3)/((1 + x^2)*(1 - 2*x^2)).

E.g.f.: (8*cosh(sqrt(2)*x) - 2*cos(x) + 5*sqrt(2)*sinh(sqrt(2)*x) - 4*sin(x))/6. (End)

3*a(n) = A228826(n+1) +A094958(n+3). - R. J. Mathar, Jan 25 2023