OFFSET
0,3
COMMENTS
LINKS
Oboifeng Dira, A Note on Composition and Recursion, Southeast Asian Bulletin of Mathematics (2017), Vol. 41, Issue 6, 849-853.
Index entries for linear recurrences with constant coefficients, signature (4,-4).
FORMULA
G.f.: (1-4x)/(1-2x)^2.
a(n) = -A058922(n). - Jeffrey R. Goodwin, Nov 11 2011
E.g.f.: U(0) where U(k)= 1 - 2*x/(2 - 4/(2 - (k+1)/U(k+1))) ; (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 18 2012
a(n) = Sum_{k=0..n} (1-2k) * C(n,k). - Wesley Ivan Hurt, Sep 23 2017
From Amiram Eldar, Jan 13 2021: (Start)
Sum_{n>=2} 1/a(n) = -log(2)/2.
Sum_{n>=2} (-1)^n/a(n) = -log(3/2)/2. (End)
MATHEMATICA
LinearRecurrence[{4, -4}, {1, 0}, 30] (* Harvey P. Dale, May 02 2016 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Apr 28 2009
STATUS
approved