cp's OEIS Frontend

A165417 a(0) = a(1) = 1. For n >=2, a(n) = sum a(k), where k is over the distinct values of the substrings in binary n, and where 0 <= k < n.

%I A165417 #7 Mar 11 2014 01:32:47
%S A165417 1,1,2,1,4,4,5,2,8,8,8,9,14,14,12,4,16,16,16,17,20,16,23,20,36,36,36,
%T A165417 37,42,42,28,8,32,32,32,33,32,36,39,36,48,48,32,42,64,60,57,44,88,88,
%U A165417 88,89,96,88,97,96,128,128,128,130,116,116,64,16,64,64,64,65,64,68,71,68,72
%N A165417 a(0) = a(1) = 1. For n >=2, a(n) = sum a(k), where k is over the distinct values of the substrings in binary n, and where 0 <= k < n.
%C A165417 The distinct nonnegative values of the substrings of binary n is row n of table A119709.
%C A165417 a(2^n) = 2^n, for all n.
%e A165417 9 in binary is 1001. The distinct nonnegative integers that occur as substrings in binary 9 are 0, 1, 2 (10 in binary), 4 (100 in binary), and 9 (1001 in binary). So a(9) = a(0)+a(1)+a(2)+a(4) = 1 + 1 + 2 + 4 = 8.
%Y A165417 Cf. A119709, A165418.
%K A165417 base,nonn
%O A165417 0,3
%A A165417 _Leroy Quet_, Sep 17 2009
%E A165417 Extended by _Ray Chandler_, Mar 13 2010