A079070 -id:A079070 - cp's OEIS frontend

A079071 Number of numbers < n whose binary representation has the same number of 0's and 1's as n does.

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

Offset: 0

Reinhard Zumkeller, Dec 21 2002

Alois P. Heinz, Table of n, a(n) for n = 0..16383

Cf. A079070, A068076, A079074, A007088, A023416, A000120.

f:= n-> (x-> (t-> t*(t+1)/2+x[2])(x[1]+x[2]))(add(
    `if`(i=0, [1, 0], [0, 1]), i=convert(n, base, 2))):
b:= proc(n) b(n):= b(n-1)+x^f(n) end: b(-1):=0:
a:= n-> coeff(b(n-1), x, f(n)):
seq(a(n), n=0..150);  # Alois P. Heinz, Feb 08 2018

a[n_] := Count[Range[n-1], k_ /; DigitCount[n, 2] == DigitCount[k, 2]];
Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Feb 13 2018 *)

A079072 Sum of numbers < n having in binary representation the same number of 0's as n.

Original entry on oeis.org

0, 0, 0, 1, 0, 2, 7, 4, 0, 4, 13, 13, 23, 24, 37, 11, 0, 8, 25, 35, 43, 54, 75, 51, 63, 97, 122, 74, 148, 101, 130, 26, 0, 16, 49, 87, 83, 122, 159, 176, 119, 197, 238, 215, 280, 258, 303, 160, 159, 324, 373, 349, 423, 400, 453, 207, 475, 507, 564, 262, 622, 321, 382, 57, 0

Offset: 0

Reinhard Zumkeller, Dec 21 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..16383

Cf. A079073, A079074, A079070, A007088, A023416.

f:= n-> add(1-i, i=convert(n, base, 2)):
b:= proc(n) b(n):= b(n-1)+n*x^f(n) end: b(-1):=0:
a:= n-> coeff(b(n-1), x, f(n)):
seq(a(n), n=0..150);  # Alois P. Heinz, Feb 08 2018

snbr[n_]:=Module[{dc=DigitCount[n,2,0]},Total[Select[Range[n-1], DigitCount[ #,2,0]==dc&]]]; Array[snbr,70] (* Harvey P. Dale, May 03 2012 *)

cp's OEIS Frontend

A079071 Number of numbers < n whose binary representation has the same number of 0's and 1's as n does.

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