A291037 a(n) = (1/2)*A291036(n).
1, 3, 8, 23, 66, 188, 537, 1533, 4376, 12493, 35664, 101812, 290649, 829731, 2368680, 6762003, 19303866, 55107824, 157319377, 449108397, 1282094784, 3660067465, 10448598672, 29828197224, 85152217777, 243088784019, 693959105912, 1981083753503, 5655510252642
Offset: 0
Links
- Clark Kimberling, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, -2, 0, -1)
Programs
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Mathematica
z = 60; s = x/(x - x^3); p = 1 - 2 s - 2 s^2; Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A079978 *) u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291036 *) u/2 (* A291037 *) LinearRecurrence[{2,2,2,-2,0,-1},{1,3,8,23,66,188},30] (* Harvey P. Dale, Sep 24 2017 *)
Formula
G.f.: -((-1 - x + x^3)/(1 - 2 x - 2 x^2 - 2 x^3 + 2 x^4 + x^6)).
a(n) = 2*a(n-1) + 2*a(n-2) + 2*a(n-3) - 2*a(n-4) - a(n-6) for n >= 7.