A038871 Triangle read by rows: T(n,k) = number of orbits of order k under doubling map which remain in a semicircle, with k dividing n.

0, 1, 1, 3, 1, 5, 7, 1, 5, 11, 15, 1, 9, 21, 27, 31, 1, 9, 21, 43, 55, 63, 1, 17, 37, 85, 91, 119, 127, 1, 17, 73, 85, 171, 219, 239, 255, 1, 33, 73, 165, 341, 363, 439, 495, 511, 1, 33, 137, 293, 341, 683, 731, 887, 991, 1023, 1, 65, 273, 585, 661, 1365, 1387

Offset

1,4

Links

Table of n, a(n) for n=1..63.

Formula

Apparently T(n, k) = Sum_{j=0..n-1} 2^floor(n*j/k), for 0 <= k <= n - 2 with T(1,0)=0. - Sean A. Irvine, Feb 16 2021

Example

From Sean A. Irvine, Feb 16 2021: (Start)
Triangle begins:
  0;
  1;
  1, 3;
  1, 5, 7;
  1, 5, 11, 15;
  1, 9, 21, 27, 31;
  1, 9, 21, 43, 55, 63;
  1, 17, 37, 85, 91, 119, 127;
  1, 17, 73, 85, 171, 219, 239, 255;
  1, 33, 73, 165, 341, 363, 439, 495, 511;
  ...
(End)

Crossrefs

Cf. A038870.

Sequence in context: A278032 A016600 A130418 * A209819 A193648 A221881

Adjacent sequences: A038868 A038869 A038870 * A038872 A038873 A038874

Keyword

nonn,tabf,easy

Author

Francois Maurel (maurel(AT)sequoia.ens.fr)

Status

approved