A290905 a(n) = (1/2)*A290904(n).

0, 1, 4, 12, 36, 111, 344, 1064, 3288, 10161, 31404, 97060, 299980, 927135, 2865456, 8856144, 27371312, 84595361, 261455316, 808068924, 2497464564, 7718808463, 23856195976, 73731339384, 227878342920, 704293989585, 2176731748220, 6727533066836, 20792502889884

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, -4, 4, -1)

Crossrefs

Cf. A000027, A290890, A290904.

Programs

Mathematica

z = 60; s = x/(1 - x)^2; p = 1 - 2 s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000027 *)
u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A290904 *)
u/2 (* A290905 *)

Formula

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

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

a(n) = (1/2)*A290904(n) for n >= 0.