cp's OEIS Frontend

A382727 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 11.

%I A382727 #15 Aug 13 2025 21:34:54
%S A382727 1,3,6,10,15,21,28,36,45,55,66,68,72,78,86,96,108,122,138,156,176,198,
%T A382727 201,207,216,228,243,261,282,306,333,363,396,400,408,420,436,456,480,
%U A382727 508,540,576,616,660,665,675,690,710,735,765,800,840,885,935,990,996,1008,1026,1050,1080,1116,1158,1206,1260,1320,1386,1393,1407
%N A382727 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 11.
%H A382727 Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2408.06817">Periodic minimum in the count of binomial coefficients not divisible by a prime</a>, arXiv:2408.06817 [math.NT], 2024.
%o A382727 (Python)
%o A382727 from math import prod
%o A382727 from gmpy2 import digits
%o A382727 def A382727(n): return sum(prod(int(d,11)+1 for d in digits(m,11)) for m in range(n+1)) # _Chai Wah Wu_, Aug 10 2025
%o A382727 (Python)
%o A382727 from math import prod
%o A382727 from gmpy2 import digits
%o A382727 def A382727(n):
%o A382727     d = list(map(lambda x:int(x,11)+1,digits(n+1,11)[::-1]))
%o A382727     return sum((b-1)*prod(d[a:])*66**a for a, b in enumerate(d))>>1 # _Chai Wah Wu_, Aug 13 2025
%Y A382727 Cf. A001316, A006046-A006048, A194458, A194459, A382720-A382731.
%K A382727 nonn
%O A382727 0,2
%A A382727 _N. J. A. Sloane_, Apr 23 2025