cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A268514 a(0)=0; thereafter a(2n+1)=3*a(n)+1, a(2n)=2*a(n)+a(n-1)+1.

Original entry on oeis.org

0, 1, 3, 4, 8, 10, 12, 13, 21, 25, 29, 31, 35, 37, 39, 40, 56, 64, 72, 76, 84, 88, 92, 94, 102, 106, 110, 112, 116, 118, 120, 121, 153, 169, 185, 193, 209, 217, 225, 229, 245, 253, 261, 265, 273, 277, 281, 283, 299, 307, 315, 319, 327, 331, 335, 337
Offset: 0

Views

Author

N. J. A. Sloane, Feb 07 2016

Keywords

Links

Crossrefs

Cf. A064194, A023416 (no. of 0's in n).
First differences are (essentially) A080100.

Programs

  • PARI
    a(n) = sum(i=1, n, b=binary(i); 2^(#b-norml2(b))) \\ Colin Barker, Feb 08 2016

Formula

a(n) = Sum{i=1..n} 2^{number of 0's in binary expansion of i}.
a(n) = (A064194(n+1)-1)/2.

A086845 a(1) = 0, a(n) = a(floor(n/2)) + 2*a(ceiling(n/2)) + floor(n/2).

Original entry on oeis.org

0, 1, 3, 5, 9, 12, 16, 19, 27, 32, 38, 42, 50, 55, 61, 65, 81, 90, 100, 106, 118, 125, 133, 138, 154, 163, 173, 179, 191, 198, 206, 211, 243, 260, 278, 288, 308, 319, 331, 338, 362, 375, 389, 397, 413, 422, 432, 438, 470, 487, 505, 515, 535
Offset: 1

Views

Author

Ralf Stephan, Aug 09 2003

Keywords

Comments

Number of comparators used in Bose-Nelson networks.
Conjecture: partial sums of A087808. - Sean A. Irvine, Jul 14 2022

Links

Crossrefs

Cf. A064194.

Programs

  • Magma
    [n le 1 select 0 else Self(Floor(n/2)) + 2*Self(Ceiling(n/2)) + Floor(n/2): n in [1..60]]; // Vincenzo Librandi, Aug 30 2016
  • PARI
    a(n)=if(n<2,0,a(floor(n/2))+2*a(ceil(n/2))+floor(n/2))
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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