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A329714 Irregular table read by rows: Take a heptagon with all diagonals drawn, as in A329713. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

%I A329714 #26 May 14 2020 04:24:50
%S A329714 35,7,7,0,1,504,224,112,28,2331,1883,1008,273,92,7,7658,6314,3416,798,
%T A329714 182,28,18662,17514,8463,2898,714,175,28,7,0,0,0,1,40404,35462,18508,
%U A329714 5796,1330,266,28
%N A329714 Irregular table read by rows: Take a heptagon with all diagonals drawn, as in A329713. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.
%C A329714 See the links in A329713 for images of the heptagons.
%H A329714 Lars Blomberg, <a href="/A329714/b329714.txt">Table of n, a(n) for n = 1..251</a> (the first 27 rows)
%e A329714 A heptagon with no other points along its edges, n = 1, contains 35 triangles, 7 quadrilaterals, 7 pentagons, 1 heptagon and no other n-gons, so the first row is [35,7,7,0,1]. A heptagon with 1 point dividing its edges, n = 2, contains 504 triangles, 224 quadrilaterals, 112 pentagons, 28 hexagons and no other n-gons, so the second row is [504,224,112,28].
%e A329714 Triangle begins:
%e A329714 35, 7, 7, 0, 1;
%e A329714 504, 224, 112, 28;
%e A329714 2331, 1883, 1008, 273, 92, 7;
%e A329714 7658, 6314, 3416, 798, 182, 28;
%e A329714 18662, 17514, 8463, 2898, 714, 175, 28, 7, 0, 0, 0, 1;
%e A329714 40404, 35462, 18508, 5796, 1330, 266, 28;
%e A329714 73248, 71596, 35777, 11669, 2654, 651, 70, 49;
%e A329714 The row sums are A329713.
%Y A329714 Cf. A329713 (regions), A333112 (edges), A333113 (vertices), A331906, A007678, A092867, A331452.
%K A329714 nonn,tabf
%O A329714 1,1
%A A329714 _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 07 2020