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A331455 Number of regions in a "cross" of width 3 and height n (see Comments for definition). 5
64, 104, 176, 304, 492, 778, 1176, 1732, 2446, 3416, 4614, 6172, 8060, 10340, 13052, 16388, 20228, 24852, 30134, 36206, 43076, 51092, 60010, 70186, 81498, 94180, 108140, 123938, 141074, 160308, 181320, 204328, 229288, 256574, 285856, 318124, 352838, 390338 (list; graph; refs; listen; history; text; internal format)
This "cross" of height n consists of a vertical column of n >= 2 squares with two additional squares extending to the left and right of the second square. (See illustrations.)
There are n+2 squares in all. The number of vertices is 3*n+2.
Now join every pair of vertices by a line segment, provided the line does not extend beyond the boundary of the cross. The sequence gives the number of regions in the resulting figure.
N. J. A. Sloane, Illustration for cross of height 3. (One of the "arms" has been cropped by the scanner, but all four arms are the same.)
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.
Cf. A330848 (n-gons), A330850 (vertices), A330851 (edges).
See A331456 for crosses in which the arms have equal length.
A331452 is a similar sequence for a rectangular region; A007678 for a polygonal region.
Sequence in context: A316419 A306165 A317382 * A039481 A094682 A118158
a(11) and beyond from Lars Blomberg, May 31 2020

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Last modified May 23 22:02 EDT 2024. Contains 372765 sequences. (Running on oeis4.)