A291733 a(n) = (1/4)*A291732(n).

1, 3, 9, 26, 72, 195, 520, 1368, 3560, 9184, 23520, 59860, 151536, 381840, 958256, 2396192, 5972736, 14845040, 36801792, 91021056, 224642304, 553347072, 1360598016, 3340024384, 8186748160, 20038426368, 48983457024, 119593531904, 291657627648, 710522702592

Offset

0,2

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4, -4, 4, -8, 0, -4)

Formula

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

a(n) = 4*a(n-1) - 4*a(n-2) + 4*a(n-3) - 8*a(n-4) - 4*a(n-6) for n >= 7.

Mathematica

z = 60; s = x + x^3; p = (1 - 2 s)^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A154272 *)
u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A291732 *)
u / 4  (*A291733)

Crossrefs

Cf. A154272, A291728, A291732.

Sequence in context: A121286 A072863 A054963 * A118046 A057153 A084787

Adjacent sequences: A291730 A291731 A291732 * A291734 A291735 A291736

Keyword

nonn,easy

Author

Clark Kimberling, Sep 11 2017

Status

approved