A291731 a(n) = (1/2)*A291730(n)..

1, 3, 9, 28, 84, 255, 772, 2340, 7088, 21476, 65064, 197126, 597228, 1809420, 5481980, 16608712, 50319264, 152451844, 461882016, 1399359936, 4239628608, 12844765920, 38915675520, 117902483528, 357208128400, 1082230358448, 3278823900048, 9933824239744

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, 4, 0, 2)

Formula

G.f.: -(((1 + x^2) (1 + x + x^3))/(-1 + 2 x + 2 x^2 + 2 x^3 + 4 x^4 + 2 x^6)).

a(n) = 4*a(n-1) + 2*a(n-2) - 4*a(n-3) - 2*a(n-4) for n >= 5.

Mathematica

z = 60; s = x + x^3; p = 1 - 2 s - 2 s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A154272 *)
u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A291730 *)
u / 2  (*A291731)

Crossrefs

Cf. A154272, A291728, A291730.

Sequence in context: A292328 A027090 A033139 * A291257 A005354 A084084

Adjacent sequences: A291728 A291729 A291730 * A291732 A291733 A291734

Keyword

nonn,easy

Author

Clark Kimberling, Sep 11 2017

Status

approved