A290865 a(n) = number of regions in the configuration A290447(n).

0, 1, 3, 7, 15, 30, 56, 98, 161, 250, 370, 536, 748, 1027, 1379, 1807, 2320, 2954, 3702, 4604, 5652, 6852, 8239, 9858, 11683, 13748, 16086, 18700, 21604, 24887, 28471, 32491, 36907, 41751, 47080, 52876, 59105, 65965, 73440, 81521, 90176

Offset

1,3

Links

David Applegate, Table of n, a(n) for n = 1..100

M. F. Hasler, Interactive web page for drawing the illustration for a(n).

N. J. A. Sloane (in collaboration with Scott R. Shannon), Art and Sequences, Slides of guest lecture in Math 640, Rutgers Univ., Feb 8, 2020. Mentions this sequence.

Example

With 3 points, there are 3 semicircles above the baseline, which bound a(3) = 3 regions. With 4 points, there are 6 semicircles, defining 7 regions (use the Halser webpage with n = 3 and 4). - N. J. A. Sloane, Aug 12 2017

Crossrefs

Cf. A290447, A290866, A290867, A332723 (number of regions with k edges).

See also A290876.

Sequence in context: A002545 A153114 A325664 * A055795 A058695 A228447

Adjacent sequences: A290862 A290863 A290864 * A290866 A290867 A290868

Keyword

nonn

Author

David Applegate, Aug 12 2017

Status

approved