A291385 a(n) = (1/4)*A073388(n+1).

1, 4, 14, 47, 152, 480, 1488, 4548, 13744, 41152, 122272, 360944, 1059584, 3095552, 9005568, 26101824, 75404544, 217191424, 623928832, 1788071680, 5113137152, 14592352256, 41569120256, 118219097088, 335685021696, 951817715712, 2695241605120, 7622609858560

Offset: 0

Author

Clark Kimberling, Sep 04 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 (4,0,-8,-4)

Crossrefs

Cf. A019590, A291382, A073388, A155112.

Programs

Mathematica

z = 60; s = x + x^2; p = (1 - 2 s)^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A019590 *)
u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A073388 *)
u / 2  (* A291385 *)
LinearRecurrence[{4,0,-8,-4},{1,4,14,47},30] (* Harvey P. Dale, Aug 24 2022 *)

Formula

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

a(n) = 4*a(n-1) - 8*a(n-3) + 4*a(n-4) for n >= 5.

a(n) = Sum_{k=0..n+1} k * A155112(n+1,k). - Alois P. Heinz, Sep 29 2022