OFFSET
0,2
COMMENTS
It appears that, except for term a(1)=2, these are the indices for which the Hankel transform of the coefficients of (1 - x)^(1/3) on F2[x] are non vanishing. See example 2.3 p. 8 of Han paper. - Michel Marcus, May 17 2020
LINKS
Guo-Niu Han, Hankel continued fraction and its applications, Advances in Mathematics, Elsevier, 2016, 303, pp.295-321. 10.1016/j.aim.2016.08.013. hal-02125293.
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).
FORMULA
a(n+1) = 2^n + 1 - a(n).
From R. J. Mathar, Feb 10 2009: (Start)
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).
a(n) = 1/2 + 2^n/3 - 5*(-1)^n/6.
G.f.: x(2-3x)/((1+x)(1-x)(1-2x)). (End)
a(n) = floor((2^n + 1)/3) + n mod 2. - Karl V. Keller, Jr., Aug 15 2021
MATHEMATICA
LinearRecurrence[{2, 1, -2}, {0, 2, 1}, 40] (* Harvey P. Dale, Mar 14 2014 *)
PROG
(Python) print([(2**n + 1)//3 + n%2 for n in range(40)]) # Karl V. Keller, Jr., Aug 15 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jan 31 2009
EXTENSIONS
Definition rephrased, more terms from R. J. Mathar, Feb 10 2009
STATUS
approved