A290912 a(n) = (1/6)*A290911(n).

0, 1, 4, 16, 68, 287, 1208, 5088, 21432, 90273, 380236, 1601584, 6745996, 28414655, 119684720, 504121280, 2123397744, 8943915201, 37672461204, 158679314512, 668369521108, 2815224014047, 11857940853032, 49946562182048, 210378775263272, 886131640451169

Offset: 0

Author

Clark Kimberling, Aug 18 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, 0, 4, -1)

Crossrefs

Cf. A000027, A290890, A290911.

Programs

GAP

a:=[0,1,4,16];; for n in [5..30] do a[n]:=4*a[n-1]+4*a[n-3]-a[n-4]; od; a; # Muniru A Asiru, Sep 12 2018

Magma

I:=[0,1,4,16]; [n le 4 select I[n] else 4*Self(n-1)+4*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Sep 13 2018

Maple

seq(coeff(series(x/(x^4-4*x^3-4*x+1),x,n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Sep 12 2018

Mathematica

z = 60; s = x/(1 - x)^2; p = 1 - 6 s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000027 *)
u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A290911 *)
u/6 (* A290912 *)
LinearRecurrence[{4,0,4,-1},{0,1,4,16},30] (* Harvey P. Dale, Sep 18 2022 *)

PARI

x='x+O('x^33); concat(0, Vec(x/(1-4*x-4*x^3+x^4))) \\ Altug Alkan, Sep 12 2018

Formula

G.f.: x/(1 - 4 x - 4 x^3 + x^4). [Corrected by A.H.M. Smeets, Sep 12 2018]

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

a(n) = (1/6)*A290911(n) for n >= 0.