OFFSET
0,1
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).
FORMULA
a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 2, a(2) = 1, a(3) = 1.
G.f.: (-2 + x^2 + 2 x^3)/(-1 + x + x^3 + x^4).
From Peter Bala, Nov 12 2019: (Start)
a(2*n) = (3/5)*Lucas(2*n) + (4/5)*(-1)^n.
a(2*n+1) = (3/5)*Lucas(2*n+1) + (7/5)*(-1)^n.
a(2*n) = a(2*n-1) + a(2*n-2) + 3*(-1)^n.
a(2*n+1) = a(2*n) + a(2*n-1) + 2*(-1)^n.
a(2*n+1)*F(n+3) - a(2*n+3)*F(n-1) = 3*F(n+1)^3, where F(n) = A000045(n). (End)
MATHEMATICA
LinearRecurrence[{1, 0, 1, 1}, {2, 2, 1, 1}, 100]
PROG
(Magma) a:=[2, 2, 1, 1]; [n le 4 select a[n] else Self(n-1) + Self(n-3) + Self(n-4):n in [1..40]]; // Marius A. Burtea, Nov 13 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 29 2017
STATUS
approved