A382723 Number of entries in the n-th row of Pascal's triangle not divisible by 4.

1, 2, 3, 4, 3, 6, 6, 8, 3, 6, 8, 12, 6, 12, 12, 16, 3, 6, 8, 12, 8, 16, 16, 24, 6, 12, 16, 24, 12, 24, 24, 32, 3, 6, 8, 12, 8, 16, 16, 24, 8, 16, 20, 32, 16, 32, 32, 48, 6, 12, 16, 24, 16, 32, 32, 48, 12, 24, 32, 48, 24, 48, 48, 64, 3, 6, 8, 12, 8, 16, 16, 24, 8, 16, 20, 32, 16, 32, 32, 48, 8

Offset: 0

Author

N. J. A. Sloane, Apr 23 2025

Keywords

• nonn

Crossrefs

Cf. A000120, A001316, A006047, A033264, A194459, A382720-A382725.

Programs

PARI

a(n) = sum(k=0, n, (binomial(n, k) % 4) != 0); \\ Michel Marcus, Apr 23 2025

Python

def A382723(n): return bin(n)[2:].count('10')+2<Chai Wah Wu, Aug 10 2025

Formula

a(n) = (A033264(n)+2)*2^(A000120(n)-1). - Chai Wah Wu, Aug 10 2025