OFFSET
0,2
COMMENTS
Equals the run length transform of A040000: 1,2,2,2,2,2,...
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.
FORMULA
a(n) = 2^A069010(n). a(2n) = a(n), a(4n+1) = 2a(n), a(4n+3) = a(2n+1). - Chai Wah Wu, Nov 04 2016
MATHEMATICA
Table[Sum[Mod[Binomial[n + 2 k, 2 k] Binomial[n, k], 2], {k, 0, n}], {n, 0, 86}] (* Michael De Vlieger, Oct 21 2016 *)
PROG
(Python)
def A277561(n):
return sum(int(not (~(n+2*k) & 2*k) | (~n & k)) for k in range(n+1))
(PARI) a(n) = sum(k=0, n, binomial(n+2*k, 2*k)*binomial(n, k) % 2); \\ Michel Marcus, Oct 21 2016
(Magma)
A277561:= func< n | (&+[(Binomial(n+2*k, 2*k)*Binomial(n, k)) mod 2 : k in [0..n]]) >;
[A277561(n): n in [0..100]]; // G. C. Greubel, Sep 06 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Oct 19 2016
STATUS
approved
