OFFSET
0,2
COMMENTS
Partial sums of A058278.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Kassie Archer and Aaron Geary, Powers of permutations that avoid chains of patterns, arXiv:2312.14351 [math.CO], 2023. See p. 15.
Engin Özkan, Bahar Kuloǧlu, and James Peters, k-Narayana sequence self-similarity, hal-03242990 [math.CO], 2021. See p. 12.
Index entries for linear recurrences with constant coefficients, signature (1,0,1).
FORMULA
G.f.: (1+x-x^2-x^3)/((1-x)*(1-x^2-x^3-x^4)) = (1+x)/(1-x-x^3);
a(n) = a(n-1) + a(n-3);
a(n) = a(n-1) + a(n-2) - a(n-5).
a(n) = A003410(n-1) for n >= 2. - Jianing Song, Aug 11 2023
MATHEMATICA
LinearRecurrence[{1, 0, 1}, {1, 2, 2}, 70] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2011*)
PROG
(PARI) a(n) = sum(k=0, n, binomial(n-k, k\2)); \\ Michel Marcus, Mar 02 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Aug 05 2004
STATUS
approved