login
A329722
a(n) = Sum_{k=0..n} ((binomial(n+2k,2n-k)*binomial(n,k)) mod 2).
2
1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 4, 1, 1, 3, 4, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 3, 2, 2, 2, 4, 2, 2, 4, 2, 1, 1, 1, 2, 3, 3, 4, 7, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 4, 1, 1
OFFSET
0,4
COMMENTS
Run length transform of the coefficients of (1-2x^3)/(1-x-x^2), i.e., 1, 1, 2, 1, 3, 4, 7, 11, ... (1, 1 followed by the Lucas sequence A000032).
PROG
(PARI) a(n) = sum(k=0, n, lift(Mod((binomial(n+2*k, 2*n-k)*binomial(n, k)), 2))) \\ Felix Fröhlich, Nov 25 2019
(Python)
def A329722(n): return sum(int(not (~(n+2*k) & 2*n-k) | (~n & k)) for k in range(n+1)) # Chai Wah Wu, Sep 28 2021
CROSSREFS
Sequence in context: A251683 A354579 A306261 * A025430 A256972 A365708
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Nov 19 2019
STATUS
approved