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The number of regions inside a vesica piscis formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.
4

%I #13 Mar 02 2021 11:32:50

%S 1,4,24,84,236,508,1048,1820,3110,4644,7428,10520,15108,20288,27576,

%T 35632,46652,58548,74156,89992,112288,135064,163684,193572,230884,

%U 269612,316846,365496,425060,485392,558744,632888,721636,811724,918040,1025224,1151904,1279188,1427720,1575496

%N The number of regions inside a vesica piscis formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

%C The terms are from numeric computation - no formula for a(n) is currently known.

%H Scott R. Shannon, <a href="/A341877/a341877.png">Regions for n=4</a>.

%H Scott R. Shannon, <a href="/A341877/a341877_1.png">Regions for n=5</a>.

%H Scott R. Shannon, <a href="/A341877/a341877_2.png">Regions for n=10</a>.

%H Scott R. Shannon, <a href="/A341877/a341877_3.png">Regions for n=15</a>.

%H Scott R. Shannon, <a href="/A341877/a341877_4.png">Regions for n=16</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Vesica_piscis">Vesica piscis</a>.

%Y Cf. A341878 (vertices), A342152 (edges), A342153 (n-gons), A007678, A092867, A340639, A340685.

%K nonn

%O 1,2

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Feb 22 2021