A291386 a(n) = (1/3)*A099432(n+1).
2, 11, 54, 252, 1134, 4977, 21438, 91017, 381996, 1588248, 6552252, 26853687, 109438938, 443837799, 1792373346, 7211142612, 28915704810, 115603540605, 460942202070, 1833459620517, 7276826042712, 28823185892016, 113957884236024, 449793742386627
Offset: 0
Links
- Clark Kimberling, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6, -3, -18, -9)
Programs
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Mathematica
z = 60; s = x + x^2; p = (1 - 3 s)^2; Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A019590 *) u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A099432 *) u / 3 (* A291386 *) LinearRecurrence[{6,-3,-18,-9},{2,11,54,252},30] (* Harvey P. Dale, Oct 06 2017 *)
Formula
G.f.: -(((1 + x) (-2 + 3 x + 3 x^2))/(-1 + 3 x + 3 x^2)^2).
a(n) = 6*a(n-1) - 3*a(n-2) - 18*a(n-3) - 9*a(n-4) for n >= 5.