cp's OEIS Frontend

A382731 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 8.

%I A382731 #12 Aug 17 2025 07:59:41
%S A382731 1,3,6,10,15,21,28,36,41,51,60,72,83,97,111,127,132,142,155,175,188,
%T A382731 206,226,250,261,283,303,331,353,381,409,441,446,456,469,489,506,532,
%U A382731 560,600,613,639,665,701,729,769,809,857,868,890,918,962,990,1030,1074,1130,1152,1196,1236,1292,1336,1392,1448,1512,1517,1527
%N A382731 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 8.
%H A382731 James G. Huard, Blair K. Spearman, and Kenneth S. Williams, <a href="https://doi.org/10.1006/eujc.1997.0146">Pascal's triangle (mod 8)</a>, European Journal of Combinatorics 19:1 (1998), pp. 45-62.
%o A382731 (Python)
%o A382731 def A382731(n):
%o A382731     c = 0
%o A382731     for m in range(n+1):
%o A382731         n1 = m>>1
%o A382731         n2 = n1>>1
%o A382731         np = ~m
%o A382731         n100 = (n2&(~n1)&np).bit_count()
%o A382731         n110 = (n2&n1&np).bit_count()
%o A382731         n10 = (n1&np).bit_count()
%o A382731         c += ((n100+1<<3)+(n110<<1)+n10*(n10+3))<<m.bit_count()>>3
%o A382731     return c # _Chai Wah Wu_, Aug 10 2025
%Y A382731 Cf. A001316, A006046-A006048, A194458, A194459, A382720-A382730.
%K A382731 nonn,changed
%O A382731 0,2
%A A382731 _N. J. A. Sloane_, Apr 23 2025