A136494 Number of permutation symmetries in the binary expansion of n.

1, 1, 1, 2, 2, 2, 2, 6, 6, 4, 4, 6, 4, 6, 6, 24, 24, 12, 12, 12, 12, 12, 12, 24, 12, 12, 12, 24, 12, 24, 24, 120, 120, 48, 48, 36, 48, 36, 36, 48, 48, 36, 36, 48, 36, 48, 48, 120, 48, 36, 36, 48, 36, 48, 48, 120, 36, 48, 48, 120, 48, 120, 120, 720, 720

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1023

Formula

a(n) = A093659(n) * A139329(n).

a(n) = A000120(n)! * A080791(n)!.

Example

a(14) = 6 because there are 3! permutation symmetries of 1's * the 0! permutation symmetries of 0's.

Mathematica

a[n_] := Times @@ (DigitCount[n, 2]!); Array[a, 65, 0] (* Amiram Eldar, Jul 29 2023 *)

Prog

(PARI) a(n) = {if(n==0, 1, my(w=hammingweight(n)); w!*(1+logint(n, 2)-w)!)} \\ Andrew Howroyd, Jan 12 2020

Crossrefs

Cf. A000120, A080791, A093659, A139329.

Sequence in context: A110023 A279466 A116863 * A260188 A048764 A327663

Adjacent sequences: A136491 A136492 A136493 * A136495 A136496 A136497

Keyword

base,nonn

Author

Max Sills, Apr 13 2008

Extensions

Terms a(32) and beyond from Andrew Howroyd, Jan 12 2020

Status

approved