OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Sela Fried, Even-up words and their variants, arXiv:2505.14196 [math.CO], 2025. See p. 4.
Index entries for linear recurrences with constant coefficients, signature (2,3,1).
FORMULA
a(n) = A000931(4n).
a(n) = A099529(2n).
a(n) = Sum_{k=0..n} binomial(2*n-k-1, 2*k-1).
a(n) = 2*a(n-1)+3*a(n-2)+a(n-3), a(0)=1, a(1)=0, a(2)=2 for n>=3.
G.f.: (1 - 2*x - x^2) / (1 - 2*x - 3*x^2 - x^3). - Colin Barker, Apr 27 2020
EXAMPLE
For n=3, a(3) = 2*a(2) + 3*a(1) + a(0) = 2*2 + 3*0 + 1 = 5.
MATHEMATICA
LinearRecurrence[{2, 3, 1}, {1, 0, 2}, 30] (* Paolo Xausa, Jul 06 2026 *)
PROG
(PARI) Vec((1 - 2*x - x^2) / (1 - 2*x - 3*x^2 - x^3) + O(x^30)) \\ Colin Barker, Apr 27 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Oboifeng Dira, Apr 21 2020
STATUS
approved