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A342153 Irregular table read by rows: Take a vesica piscis with all diagonals drawn, as in A341877. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

%I A342153 #9 Mar 02 2021 11:33:46
%S A342153 0,4,18,6,52,28,4,120,78,34,4,252,188,56,12,470,348,184,40,4,2,808,
%T A342153 648,300,56,8,1282,1118,548,138,20,4,2036,1772,644,156,28,8,2878,2804,
%U A342153 1252,388,96,10,4172,4024,1728,468,100,28,5752,5682,2600,866,162,46,7912,7676,3420,1024,196,44,16
%N A342153 Irregular table read by rows: Take a vesica piscis with all diagonals drawn, as in A341877. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.
%C A342153 The terms are from numeric computation - no formula for a(n) is currently known.
%C A342153 See A341877 for images of the regions and A341878 for images of the vertices.
%H A342153 Scott R. Shannon, <a href="/A342153/a342153.png">Image of the k-gons for n=14</a>.
%H A342153 Wikipedia, <a href="https://en.wikipedia.org/wiki/Vesica_piscis">Vesica piscis</a>.
%e A342153 A vesica piscis with 1 point dividing its edges, n = 2, contains 4 triangles and no other n-gons, so the second row is [4]. A vesica piscis with 3 points dividing its edges, n = 4, contains 52 triangles, 28 quadrilaterals, 4 pentagons and no other n-gons, so the fourth row is [52, 28, 4].
%e A342153 The table begins:
%e A342153 0;
%e A342153 4;
%e A342153 18,6;
%e A342153 52,28,4;
%e A342153 120,78,34,4;
%e A342153 252,188,56,12;
%e A342153 470,348,184,40,4,2;
%e A342153 808,648,300,56,8;
%e A342153 1282,1118,548,138,20,4;
%e A342153 2036,1772,644,156,28,8;
%e A342153 2878,2804,1252,388,96,10;
%e A342153 4172,4024,1728,468,100,28;
%e A342153 5752,5682,2600,866,162,46;
%e A342153 7912,7676,3420,1024,196,44,16;
%e A342153 10388,10354,4868,1548,352,60,6;
%e A342153 13496,13808,6016,1836,388,80,4,0,4;
%e A342153 17310,17590,8376,2672,564,122,16,2;
%e A342153 22012,22364,10160,3152,712,124,20,4;
%e A342153 27440,27956,13162,4432,964,172,24,2,4;
%e A342153 33784,34736,15588,4640,1096,120,28;
%Y A342153 Cf. A341877 (regions), A342152 (edges), A341878 (vertices), A331451, A331911, A340614, A340688.
%K A342153 nonn,tabf
%O A342153 1,2
%A A342153 _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 02 2021