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A368844 a(n) gives the number of triples of equally spaced 0's in the binary expansion of n (without leading zeros).

%I A368844 #14 Jan 10 2024 12:12:31
%S A368844 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,2,
%T A368844 2,1,0,0,0,0,2,0,1,0,0,0,0,0,2,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,6,4,3,2,
%U A368844 2,2,1,1,2,0,1,0,0,0,0,0,3,2,0,0,1,1,0
%N A368844 a(n) gives the number of triples of equally spaced 0's in the binary expansion of n (without leading zeros).
%H A368844 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A368844 a(2*n) >= a(n).
%F A368844 a(2*n + 1) = a(n).
%e A368844 For n = 277:
%e A368844 - the binary expansion of 277 is "100010101",
%e A368844 - we have the following triples:   000
%e A368844                                    0 0 0
%e A368844                                      0 0 0
%e A368844 - so a(277) = 3.
%o A368844 (PARI) a(n, t = 0, base = 2) = { my (d = digits(n, base), v = 0); for (i = 1, #d-2, if (d[i]==t, forstep (j = i+2, #d, 2, if (d[i]==d[j] && d[i]==d[(i+j)/2], v++;);););); return (v); }
%o A368844 (Python)
%o A368844 def A368844(n):
%o A368844     l = len(s:=bin(n)[3:])
%o A368844     return sum(1 for i in range(l-2) for j in range(1,l-i+1>>1) if s[i:i+(j<<1)+1:j]=='000') # _Chai Wah Wu_, Jan 10 2024
%Y A368844 Cf. A368842, A368843.
%K A368844 nonn,base,easy
%O A368844 0,17
%A A368844 _Rémy Sigrist_, Jan 07 2024