A303065 - OEIS

%I #11 May 26 2018 17:25:36

%S 0,0,0,0,1,1,2,0,0,1,2,1,3,2,3,0,0,2,3,3,4,4,5,1,5,6,7,2,8,3,4,0,0,1,

%T 2,4,3,5,6,4,4,7,8,5,9,6,7,1,5,10,11,8,12,9,10,2,13,11,12,3,13,4,5,0,

%U 0,1,2,6,3,7,8,9,4,9,10,10,11,11,12,5,5,12,13

%N Number of numbers < n whose binary representation has the same difference between the numbers of 0's and 1's as n does.

%C First occurrence of k, k=0,1,2,...: 0, 4, 6, 12, 20, 22, 25, 26, 28, 44, 49, ..., . - _Robert G. Wilson v_, Feb 08 2018

%F a(n) = 0 iff n belongs to A097110. - _Rémy Sigrist_, May 16 2018

%e There are two numbers below 6 with number of 1's in the binary representation minus number of 0's equal to 1, namely 1 and 5, therefore a(6)=2.

%e There are 3 numbers below 12 with number of 1's in the binary representation minus number of 0's equal to 0, namely 2, 9, 10, therefore a(12)=3.

%t d[n_] := DigitCount[n, 2, 1] - DigitCount[n, 2, 0]; f[n_] := Block[{fd = d[n], c = k = 0}, While[k < n, If[d@ k == fd, c++]; k++]; c]; Array[f, 83, 0] (* _Robert G. Wilson v_, Feb 08 2018 *)

%o (Python)

%o d=[0]*200

%o for n in range(1024):

%o     b = bin(n)[2:]

%o     c0 = b.count('0')

%o     c1 = len(b) - c0

%o     diff = c0 - c1

%o     print str(d[100+diff])+',',

%o     d[100+diff] += 1

%Y Cf. A037861, A097110.

%K nonn,base

%O 1,7

%A _Alex Ratushnyak_, Apr 17 2018