A291406 a(n) = (1/2)A291405(n).

0, 1, 2, 4, 12, 26, 60, 145, 336, 796, 1880, 4412, 10400, 24488, 57648, 135794, 319744, 752908, 1773016, 4175032, 9831472, 23151400, 54516976, 128377380, 302304640, 711870368, 1676321856, 3947423264, 9295440640, 21889019712, 51544533376, 121377706184

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0, 2, 4, 4, 8, 12, 8, 2)

Formula

G.f.: -((x (1 + x)^2 (1 + x^2 + 2 x^3 + x^4))/(-1 + 2 x^2 + 4 x^3 + 4 x^4 + 8 x^5 + 12 x^6 + 8 x^7 + 2 x^8)).

a(n) = 2*a(n-2) + 4*a(n-3) + 4*a(n-4) + 5*a(n-5) + 12*a(n-6) + 8*a(n-7) + 2*a(n-8) for n >= 9.

Mathematica

z = 60; s = x + x^2; p = 1 - 2 s^2 - 2 s^4;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A019590 *)
u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A291405 *)
u / 2 (* A291406 *)

Crossrefs

Cf. A019590, A291382, A291405.

Sequence in context: A284125 A045678 A236002 * A219752 A242536 A027132

Adjacent sequences: A291403 A291404 A291405 * A291407 A291408 A291409

Keyword

nonn,easy

Author

Clark Kimberling, Sep 07 2017

Status

approved