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

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..10000

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.

Maple

Res:= 1, 2: P:= [1, 1]:
for n from 2 to 100 do
  P:= [1, op(P[2..-1]+P[1..-2] mod 8), 1];
  Res:= Res, n +1 - numboccur(0, P)
od:
Res; # Robert Israel, Mar 15 2026

Prog

(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))<<n.bit_count()>>3 # Chai Wah Wu, Aug 10 2025

Crossrefs

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

Sequence in context: A245350 A307282 A245354 * A097377 A234741 A063917

Adjacent sequences: A382722 A382723 A382724 * A382726 A382727 A382728

Keyword

nonn

Author

N. J. A. Sloane, Apr 23 2025

Status

approved