

A332953


The number of regions formed inside an isosceles triangle by straight line segments mutually connecting all vertices and all points that divide the two equal length sides into n equal parts; the base of the triangle contains no points other than its vertices.


7



1, 5, 18, 52, 125, 257, 486, 832, 1333, 2027, 3048, 4304, 6057, 8167, 10749, 13929, 18058, 22664, 28533, 34981, 42519, 51425, 62118, 73473, 86768, 101902, 118695, 137138, 159147, 181752, 208813, 237209, 268614, 303718, 340882, 380811, 427540, 477134, 530047
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OFFSET

1,2


COMMENTS

The terms are from numeric computation  no formula for a(n) is currently known.
Equivalently, this is also the number of regions formed when all the integer points along the x and y axes with 0 <= x <= n and 0 <= y <= n are joined by straight line segments.
If instead one takes points on the x and y axes with coordinates 1, 1/2, 1/3, 1/4, ..., 1/n, 0, and joins them all by line segments, the resulting figure contains only triangles and quadrilaterals, and the number of regions is given by A332358 (and more generally by A332357 if there are m+1 such points on the x axis and n+1 such points on the y axis).


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CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



