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A332723 Irregular table read by rows: Take a line with n equally spaced points with semicircles drawn between them, as in A290447. Then T(n,k) = number of k-sided regions in that figure, where k>=2.

%I A332723 #29 Jul 20 2020 18:57:13
%S A332723 1,2,1,3,4,4,10,0,1,5,19,3,3,6,31,13,6,7,46,35,10,8,65,74,14,9,92,131,
%T A332723 18,10,140,192,27,1,11,202,274,46,3,12,275,396,62,3,13,363,563,79,9,
%U A332723 14,467,784,100,14,15,598,1054,126,12,2
%N A332723 Irregular table read by rows: Take a line with n equally spaced points with semicircles drawn between them, as in A290447. Then T(n,k) = number of k-sided regions in that figure, where k>=2.
%H A332723 Scott R. Shannon, <a href="/A332723/b332723.txt">Table of n, a(n) for n = 2..345</a>. The terms for 2 to 55 points.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723.png">Illustration of regions for n = 5</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_8.png">Illustration of regions for n = 6</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_1.png">Illustration of regions for n = 10</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_5.png">Illustration of regions for n = 11</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_2.png">Illustration of regions for n = 15</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_9.png">Illustration of regions for n = 16</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_3.png">Illustration of regions for n = 20</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_4.png">Illustration of regions for n = 21</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_6.png">Illustration of regions for n = 25</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_7.png">Illustration of regions for n = 26</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_10.png">Illustration of regions with random distance-based coloring for n = 10</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_11.png">Illustration of regions with random distance-based coloring for n = 11</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_12.png">Illustration of regions with random distance-based coloring for n = 15</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_13.png">Illustration of regions with random distance-based coloring for n = 16</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_14.png">Illustration of regions with random distance-based coloring for n = 20</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_15.png">Illustration of regions with random distance-based coloring for n = 21</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_16.png">Illustration of regions with random distance-based coloring for n = 25</a>.
%H A332723 Scott R. Shannon, <a href="/A332723/a332723_17.png">Illustration of regions with random distance-based coloring for n = 26</a>.
%e A332723 The first 25 rows are:
%e A332723 1;
%e A332723 2,1;
%e A332723 3,4;
%e A332723 4,10,0,1;
%e A332723 5,19,3,3;
%e A332723 6,31,13,6;
%e A332723 7,46,35,10;
%e A332723 8,65,74,14;
%e A332723 9,92,131,18;
%e A332723 10,140,192,27,1;
%e A332723 11,202,274,46,3;
%e A332723 12,275,396,62,3;
%e A332723 13,363,563,79,9;
%e A332723 14,467,784,100,14;
%e A332723 15,598,1054,126,12,2;
%e A332723 16,772,1358,159,13,2;
%e A332723 17,996,1698,216,24,2,1;
%e A332723 18,1255,2120,266,41,2;
%e A332723 19,1551,2629,346,54,5;
%e A332723 20,1892,3236,425,71,8;
%e A332723 21,2304,3909,525,83,9,1;
%e A332723 22,2793,4676,629,108,9,2;
%e A332723 23,3342,5559,792,125,14,3;
%e A332723 24,3982,6546,948,166,15,2;
%e A332723 25,4705,7658,1145,198,14,3;
%e A332723 The row sums are A290865.
%Y A332723 Cf. A290447, A290865, A290866, A290867, A290726.
%K A332723 nonn,tabf
%O A332723 2,2
%A A332723 _Scott R. Shannon_ and _N. J. A. Sloane_, Feb 21 2020