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A302436 a(n) is the number of ways of writing the binary expansion of n as a concatenation of nonempty substrings with Hamming weight at most 1.

%I A302436 #11 Apr 15 2018 15:03:20
%S A302436 1,1,2,1,4,3,2,1,8,7,6,3,4,3,2,1,16,15,14,7,12,9,6,3,8,7,6,3,4,3,2,1,
%T A302436 32,31,30,15,28,21,14,7,24,21,18,9,12,9,6,3,16,15,14,7,12,9,6,3,8,7,6,
%U A302436 3,4,3,2,1,64,63,62,31,60,45,30,15,56,49,42,21
%N A302436 a(n) is the number of ways of writing the binary expansion of n as a concatenation of nonempty substrings with Hamming weight at most 1.
%C A302436 Leading zeros in the binary expansion of n are ignored.
%C A302436 The value a(0) = 1 corresponds to the empty concatenation.
%C A302436 See A301453 for similar sequences.
%H A302436 Rémy Sigrist, <a href="/A302436/b302436.txt">Table of n, a(n) for n = 0..10000</a>
%F A302436 a(2^n - 1) = 1 for any n >= 0.
%F A302436 a(2^n) = 2^n for any n >= 0.
%F A302436 a(2*n) = 2*a(n) for any n > 0.
%e A302436 For n = 9: the binary expansion of 9, "1001", can be split in 7 ways into nonempty substrings with Hamming weight at most 1:
%e A302436 - (100)(1),
%e A302436 - (10)(01),
%e A302436 - (10)(0)(1),
%e A302436 - (1)(001),
%e A302436 - (1)(00)(1),
%e A302436 - (1)(0)(01),
%e A302436 - (1)(0)(0)(1).
%e A302436 Hence a(9) = 7.
%o A302436 (PARI) a(n) = if (n==0, return (1), my (v=0, h=0); while (n, h += n%2; n\=2; if (h>1, break, v+=a(n))); return (v))
%Y A302436 Cf. A301453.
%K A302436 nonn,base
%O A302436 0,3
%A A302436 _Rémy Sigrist_, Apr 08 2018