OFFSET
0,3
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)
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.
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 *)
PROG
(PARI) x='x+O('x^33); concat(0, Vec(x/(1-4*x-4*x^3+x^4))) \\ Altug Alkan, Sep 12 2018
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Aug 18 2017
STATUS
approved