A101691 A modular binomial sum sequence.

1, 1, 2, 1, 3, 1, 2, 2, 5, 1, 2, 2, 4, 2, 4, 4, 9, 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 17, 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 33, 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

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

a(2^n) = A094373(n). a(2^n-1) = 1,1,1,2,4,8,16,...

Mathematica

Table[Sum[Mod[Binomial[2n-2, k], 2], {k, 0, n}], {n, 0, 100}] (* Harvey P. Dale, Oct 20 2011 *)

Prog

(Python)
def A101691(n): return sum((not ~(n-1<<1)&k) for k in range(n+1)) # Chai Wah Wu, Jul 31 2025

Crossrefs

Cf. A048896.

Sequence in context: A037269 A124579 A035306 * A349445 A205379 A238881

Adjacent sequences: A101688 A101689 A101690 * A101692 A101693 A101694

Keyword

easy,nonn

Author

Paul Barry, Dec 11 2004

Status

approved