cp's OEIS Frontend

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

%I A387108 #8 Aug 17 2025 11:17:17
%S A387108 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,
%T A387108 12,18,24,30,15,20,25,30,35,24,28,32,36,40,33,36,39,42,45,42,44,46,48,
%U A387108 50,11,22,33,44,55,24,33,42,51,60,37,44,51,58,65,50,55,60
%N A387108 Number of entries in the n-th row of Pascal's triangle not divisible by 25.
%H A387108 Eric Rowland, <a href="https://arxiv.org/abs/1001.1783">The number of nonzero binomial coefficients modulo p^alpha</a>, arXiv:1001.1783 [math.NT]
%o A387108 (Python)
%o A387108 import re
%o A387108 from gmpy2 import digits
%o A387108 def A387108(n):
%o A387108     s = digits(n,5)
%o A387108     n1, n2, n3, n4 = s.count('1'), s.count('2'), s.count('3'), s.count('4')
%o A387108     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))
%o A387108     n20, n21, n23, n30, n22 = s.count('20'), s.count('21'), s.count('23'), s.count('30'), len(re.findall('(?=22)',s))
%o A387108     n31, n32, n40, n41, n33 = s.count('31'), s.count('32'), s.count('40'), s.count('41'), len(re.findall('(?=33)',s))
%o A387108     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
%Y A387108 Cf. A001316, A006047, A194459, A382720-A382725, A386952, A387050, A387051.
%K A387108 nonn
%O A387108 0,2
%A A387108 _Chai Wah Wu_, Aug 16 2025