A289788 a(n) = (1/2)*A289787(n).

1, 6, 31, 156, 785, 3954, 19919, 100344, 505489, 2546430, 12827791, 64620756, 325530881, 1639881066, 8260997855, 41615265264, 209639359969, 1056070674294, 5320018479679, 26799907726860, 135006120168881, 680101314855906, 3426050596003631, 17258932500172776

Offset: 0

Author

Clark Kimberling, Aug 10 2017

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6, -6, 6, -1)

Crossrefs

Cf. A289780, A289787.

Programs

Mathematica

z = 60; s = 2*x/(1 - x)^2; p = 1 - s - s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A005843 *)
u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A289787 *)
u/2 (* A289788 *)

Formula

G.f.: (1 + x^2)/(1 - 6 x + 6 x^2 - 6 x^3 + x^4).

a(n) = 6*a(n-1) - 6*a(n-2) + 6*a(n-3) - a(n-4).