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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. 4
0, 4, 18, 6, 52, 28, 4, 120, 78, 34, 4, 252, 188, 56, 12, 470, 348, 184, 40, 4, 2, 808, 648, 300, 56, 8, 1282, 1118, 548, 138, 20, 4, 2036, 1772, 644, 156, 28, 8, 2878, 2804, 1252, 388, 96, 10, 4172, 4024, 1728, 468, 100, 28, 5752, 5682, 2600, 866, 162, 46, 7912, 7676, 3420, 1024, 196, 44, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

See A341877 for images of the regions and A341878 for images of the vertices.

LINKS

Table of n, a(n) for n=1..63.

Scott R. Shannon, Image of the k-gons for n=14.

Wikipedia, Vesica piscis.

EXAMPLE

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].

The table begins:

0;

4;

18,6;

52,28,4;

120,78,34,4;

252,188,56,12;

470,348,184,40,4,2;

808,648,300,56,8;

1282,1118,548,138,20,4;

2036,1772,644,156,28,8;

2878,2804,1252,388,96,10;

4172,4024,1728,468,100,28;

5752,5682,2600,866,162,46;

7912,7676,3420,1024,196,44,16;

10388,10354,4868,1548,352,60,6;

13496,13808,6016,1836,388,80,4,0,4;

17310,17590,8376,2672,564,122,16,2;

22012,22364,10160,3152,712,124,20,4;

27440,27956,13162,4432,964,172,24,2,4;

33784,34736,15588,4640,1096,120,28;

CROSSREFS

Cf. A341877 (regions), A342152 (edges), A341878 (vertices), A331451, A331911, A340614, A340688.

Sequence in context: A205014 A204936 A158320 * A341800 A236563 A264207

Adjacent sequences:  A342150 A342151 A342152 * A342154 A342155 A342156

KEYWORD

nonn,tabf

AUTHOR

Scott R. Shannon and N. J. A. Sloane, Mar 02 2021

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)