A329722 a(n) = Sum_{k=0..n} ((binomial(n+2k,2n-k)*binomial(n,k)) mod 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).

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Chai Wah Wu, Sums of products of binomial coefficients mod 2 and run length transforms of sequences, arXiv:1610.06166 [math.CO], 2016.

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

Cf. A000032, A329723.

Sequence in context: A251683 A354579 A306261 * A025430 A256972 A365708

Adjacent sequences: A329719 A329720 A329721 * A329723 A329724 A329725

Keyword

nonn

Author

Chai Wah Wu, Nov 19 2019

Status

approved