A290907 a(n) = (1/3)*A290906(n).

0, 1, 4, 13, 44, 152, 524, 1803, 6204, 21351, 73480, 252880, 870280, 2995049, 10307396, 35472677, 122078436, 420130248, 1445868996, 4975926307, 17124540796, 58933729999, 202819133840, 697997582240, 2402143306640, 8266923285201, 28450434416004, 97911543452733

Offset: 0

Author

Clark Kimberling, Aug 17 2017

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4, -3, 4, -1)

Crossrefs

Cf. A000027, A290890, A290906.

Programs

Mathematica

z = 60; s = x/(1 - x)^2; p = 1 - 3 s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000027 *)
u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A290906 *)
u/3 (* A290907 *)

Formula

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

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

a(n) = (1/3)*A290906(n) for n >= 0.