A079072 -id:A079072 - cp's OEIS frontend

A079074 Sum of numbers < n having in binary representation the same number of 0's and 1's as n.

0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 9, 0, 19, 11, 24, 0, 0, 0, 17, 0, 35, 19, 40, 0, 55, 62, 87, 23, 113, 50, 79, 0, 0, 0, 33, 0, 67, 35, 72, 0, 103, 110, 151, 39, 193, 82, 127, 0, 143, 237, 286, 173, 336, 224, 277, 47, 388, 331, 388, 102, 446, 161, 222, 0, 0, 0, 65, 0, 131, 67, 136, 0

Offset: 0

Reinhard Zumkeller, Dec 21 2002

nonn

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

Cf. A079072, A079073, A079071, 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)+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

bdQ[m_,n_]:=Module[{a=DigitCount[m,2,0],b=DigitCount[m,2,1], c= DigitCount[ n,2,0], d=DigitCount[ n,2,1]}, a==c&&b==d]; Table[Total[ Select[Range[n-1],bdQ[#,n]&]],{n,80}] (* Harvey P. Dale, Sep 08 2011 *)

A079070 Number of numbers < n having in binary representation the same number of 0's as n.

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 2, 0, 1, 2, 3, 3, 4, 5, 3, 0, 1, 2, 4, 3, 5, 6, 6, 4, 7, 8, 7, 9, 8, 9, 4, 0, 1, 2, 5, 3, 6, 7, 10, 4, 8, 9, 11, 10, 12, 13, 10, 5, 11, 12, 14, 13, 15, 16, 11, 14, 17, 18, 12, 19, 13, 14, 5, 0, 1, 2, 6, 3, 7, 8, 15, 4, 9, 10, 16, 11, 17, 18, 20, 5, 12, 13, 19, 14, 20, 21, 21, 15

Offset: 1

Reinhard Zumkeller, Dec 21 2002

			n = 12 -> '1100': A023416(12) = 2 therefore a(12) = #{4 ->'100', 9 ->'1001', 10 ->'1010'} = 3.
n = 13 -> '1101': A023416(13) = 1 therefore a(13) = #{2 ->'10', 5 ->'101', 6 ->'110', 11 ->'1011'} = 4.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A068076, A079071, A079072, A007088, A023416.

import Data.List (elemIndices)
a079070 n = length $ elemIndices (a023416 n) $ map a023416 [1..n-1]
-- Reinhard Zumkeller, Jun 16 2011

dcn[n_]:=Count[Range[n-1],?(DigitCount[#,2,0]==DigitCount[ n,2,0]&)]; Array[dcn,90] (* _Harvey P. Dale, Jun 11 2011 *)

a(n) = #{m : m < n and A023416(m) = A023416(n)}.

a(2^k - 1) = k - 1; a(2^k) = 0; a(2^k + 1) = 1.

A079073 Sum of numbers < n having in binary representation the same number of 1's as n.

Original entry on oeis.org

0, 0, 1, 0, 3, 3, 8, 0, 7, 14, 23, 7, 33, 18, 31, 0, 15, 45, 62, 45, 80, 64, 85, 15, 100, 107, 132, 38, 158, 65, 94, 0, 31, 124, 157, 186, 191, 221, 258, 124, 227, 296, 337, 163, 379, 206, 251, 31, 267, 423, 472, 297, 522, 348, 401, 78, 574, 455, 512, 133, 570, 192, 253, 0, 63

Offset: 0

Reinhard Zumkeller, Dec 21 2002

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

Cf. A079072, A079074, A068076, A007088, A000120.

f:= n-> add(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

a[n_] := Module[{dc = DigitCount[n, 2, 1]}, Select[Range[n-1], DigitCount[#, 2, 1] == dc&] // Total];
a /@ Range[0, 100] (* Jean-François Alcover, Nov 07 2020 *)

a(n) = my(s=hammingweight(n)); sum(k=1, n-1, if (s==hammingweight(k), k)); \\ Michel Marcus, Nov 07 2020

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A079074 Sum of numbers < n having in binary representation the same number of 0's and 1's as n.

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A079070 Number of numbers < n having in binary representation the same number of 0's as n.

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A079073 Sum of numbers < n having in binary representation the same number of 1's as n.

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