A382731 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 8.

1, 3, 6, 10, 15, 21, 28, 36, 41, 51, 60, 72, 83, 97, 111, 127, 132, 142, 155, 175, 188, 206, 226, 250, 261, 283, 303, 331, 353, 381, 409, 441, 446, 456, 469, 489, 506, 532, 560, 600, 613, 639, 665, 701, 729, 769, 809, 857, 868, 890, 918, 962, 990, 1030, 1074, 1130, 1152, 1196, 1236, 1292, 1336, 1392, 1448, 1512, 1517, 1527

Offset

0,2

Links

Table of n, a(n) for n=0..65.

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.

Prog

(Python)
def A382731(n):
    c = 0
    for m in range(n+1):
        n1 = m>>1
        n2 = n1>>1
        np = ~m
        n100 = (n2&(~n1)&np).bit_count()
        n110 = (n2&n1&np).bit_count()
        n10 = (n1&np).bit_count()
        c += ((n100+1<<3)+(n110<<1)+n10*(n10+3))<<m.bit_count()>>3
    return c # Chai Wah Wu, Aug 10 2025

Crossrefs

Cf. A001316, A006046-A006048, A194458, A194459, A382720-A382730.

Sequence in context: A067525 A130487 A231684 * A363777 A108923 A033441

Adjacent sequences: A382728 A382729 A382730 * A382732 A382733 A382734

Keyword

nonn

Author

N. J. A. Sloane, Apr 23 2025

Status

approved