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A386953 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 9.

%I A386953 #12 Aug 17 2025 07:59:34
%S A386953 1,3,6,10,15,21,28,36,45,49,57,69,78,90,105,119,135,153,160,174,195,
%T A386953 209,228,252,273,297,324,328,336,348,360,378,402,422,450,486,495,513,
%U A386953 540,560,588,624,655,693,738,752,780,822,850,888,936,978,1026,1080,1087
%N A386953 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 9.
%H A386953 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 A386953 (Python)
%o A386953 import re
%o A386953 from gmpy2 import digits
%o A386953 def A386953(n):
%o A386953     c = 0
%o A386953     for m in range(n+1):
%o A386953         s = digits(m,3)
%o A386953         n1 = s.count('1')
%o A386953         n2 = s.count('2')
%o A386953         n01 = s.count('10')
%o A386953         n02 = s.count('20')
%o A386953         n11 = len(re.findall('(?=11)',s))
%o A386953         n12 = s.count('21')
%o A386953         c += ((3*((1+n01<<2)+n11)+((n02<<2)+n12<<2))*3**n2<<n1)//3>>2
%o A386953     return c
%Y A386953 Cf. A001316, A006046-A006048, A194458, A194459, A382720-A382731.
%Y A386953 Partial sums of A386952.
%K A386953 nonn
%O A386953 0,2
%A A386953 _Chai Wah Wu_, Aug 10 2025