OFFSET
0,3
COMMENTS
-a(n) is the Hankel transform of A030662(n) = binomial(2*n,n)-1.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,8,-16).
FORMULA
a(n) = 2^(n-1)*(cos(2*Pi*n/3) + sqrt(3)*sin(2*Pi*n/3)/3 + 2n - 1);
O.g.f.: x(1+2x+16x^2)/((2x-1)^2*(4x^2+2x+1)). a(n) = 2a(n-1) + 8a(n-3) - 16a(n-4). - R. J. Mathar, Apr 28 2008
MATHEMATICA
a047240[n_] := 6 Floor[n/3] + Mod[n, 3]
a128205[n_] := Map[2^(#-1) a047240[#]&, Range[0, n]]
a128205[25] (* data *) (* Hartmut F. W. Hoft, Mar 13 2017 *)
LinearRecurrence[{2, 0, 8, -16}, {0, 1, 4, 24}, 40] (* Harvey P. Dale, Feb 13 2024 *)
PROG
(PARI) concat(0, Vec(x*(1 + 2*x + 16*x^2) / ((1 - 2*x)^2*(1 + 2*x + 4*x^2)) + O(x^40))) \\ Colin Barker, Mar 13 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 19 2007
STATUS
approved