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

0,2

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)

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.

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 *)

Crossrefs

Cf. A079978, A290616, A291036.

Sequence in context: A176880 A078054 A018043 * A147704 A116410 A199841

Adjacent sequences: A291034 A291035 A291036 * A291038 A291039 A291040

Keyword

nonn,easy

Author

Clark Kimberling, Sep 14 2017

Status

approved