

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
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OFFSET

2,1


COMMENTS

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.


LINKS

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.


CROSSREFS

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.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



