A382725 Number of entries in the n-th row of Pascal's triangle not divisible by 8.

1, 2, 3, 4, 5, 6, 7, 8, 5, 10, 9, 12, 11, 14, 14, 16, 5, 10, 13, 20, 13, 18, 20, 24, 11, 22, 20, 28, 22, 28, 28, 32, 5, 10, 13, 20, 17, 26, 28, 40, 13, 26, 26, 36, 28, 40, 40, 48, 11, 22, 28, 44, 28, 40, 44, 56, 22, 44, 40, 56, 44, 56, 56, 64, 5, 10, 13, 20, 17, 26, 28, 40, 17, 34, 34, 52, 36, 56, 56, 80, 13

Offset: 0

Author

N. J. A. Sloane, Apr 23 2025

Keywords

• nonn
• changed

Links

• James G. Huard, Blair K. Spearman, and Kenneth S. Williams, Pascal's triangle (mod 8), European Journal of Combinatorics 19:1 (1998), pp. 45-62.

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382724.

Programs

Python

def A382725(n):
    n1 = n>>1
    n2 = n1>>1
    np = ~n
    n100 = (n2&(~n1)&np).bit_count()
    n110 = (n2&n1&np).bit_count()
    n10 = (n1&np).bit_count()
    return ((n100+1<<3)+(n110<<1)+n10*(n10+3))<>3 # Chai Wah Wu, Aug 10 2025