A387108 Number of entries in the n-th row of Pascal's triangle not divisible by 25.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 6, 12, 18, 24, 30, 15, 20, 25, 30, 35, 24, 28, 32, 36, 40, 33, 36, 39, 42, 45, 42, 44, 46, 48, 50, 11, 22, 33, 44, 55, 24, 33, 42, 51, 60, 37, 44, 51, 58, 65, 50, 55, 60

Offset: 0

Author

Chai Wah Wu, Aug 16 2025

Keywords

• nonn

Links

• Eric Rowland, The number of nonzero binomial coefficients modulo p^alpha, arXiv:1001.1783 [math.NT]

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382725, A386952, A387050, A387051.

Programs

Python

import re
from gmpy2 import digits
def A387108(n):
    s = digits(n,5)
    n1, n2, n3, n4 = s.count('1'), s.count('2'), s.count('3'), s.count('4')
    n10, n12, n13, n42, n43, n11 = s.count('10'), s.count('12'), s.count('13'), s.count('42'), s.count('43'), len(re.findall('(?=11)',s))
    n20, n21, n23, n30, n22 = s.count('20'), s.count('21'), s.count('23'), s.count('30'), len(re.findall('(?=22)',s))
    n31, n32, n40, n41, n33 = s.count('31'), s.count('32'), s.count('40'), s.count('41'), len(re.findall('(?=33)',s))
    return ((1440*n10+540*n11+240*n12+90*n13+1920*n20+720*(n21+1)+320*n22+120*n23+2160*n30+810*n31+360*n32+135*n33+2304*n40+864*n41+384*n42+144*n43)*3**n2*5**n4<<(n1+(n3<<1)))//45>>4