A079073 -id:A079073 - cp's OEIS frontend

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

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 *)

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

Original entry on oeis.org

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 *)

cp's OEIS Frontend

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

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