cp's OEIS Frontend

A386952 Number of entries in the n-th row of Pascal's triangle not divisible by 9.

%I A386952 #12 Aug 17 2025 07:59:29
%S A386952 1,2,3,4,5,6,7,8,9,4,8,12,9,12,15,14,16,18,7,14,21,14,19,24,21,24,27,
%T A386952 4,8,12,12,18,24,20,28,36,9,18,27,20,28,36,31,38,45,14,28,42,28,38,48,
%U A386952 42,48,54,7,14,21,20,31,42,33,48,63,14,28,42,31,44,57,48
%N A386952 Number of entries in the n-th row of Pascal's triangle not divisible by 9.
%H A386952 James G. Huard, Blair K. Spearman, and Kenneth S. Williams, <a href="http://doi.org/10.4064/aa-78-4-331-349">Pascal's triangle (mod 9)</a>, Acta Arithmetica, 78 (1997), 331-349.
%o A386952 (Python)
%o A386952 import re
%o A386952 from gmpy2 import digits
%o A386952 def A386952(n):
%o A386952     s = digits(n,3)
%o A386952     n1 = s.count('1')
%o A386952     n2 = s.count('2')
%o A386952     n01 = s.count('10')
%o A386952     n02 = s.count('20')
%o A386952     n11 = len(re.findall('(?=11)',s))
%o A386952     n12 = s.count('21')
%o A386952     return ((3*((1+n01<<2)+n11)+((n02<<2)+n12<<2))*3**n2<<n1)//3>>2
%Y A386952 Cf. A001316, A006047, A194459, A382720-A382725.
%K A386952 nonn
%O A386952 0,2
%A A386952 _Chai Wah Wu_, Aug 10 2025