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A291385
a(n) = (1/4)*A073388(n+1).
2
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
0,2
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
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 04 2017
STATUS
approved