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A333076 Irregular table read by rows: Take an octagon with all diagonals drawn, as in A333075. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

%I A333076 #16 Aug 26 2020 01:58:23
%S A333076 56,24,800,608,64,16,4136,3400,1272,464,40,13840,10800,5296,1264,288,
%T A333076 64,33160,30048,14744,4456,840,152,32,70832,62208,30848,8656,1936,288,
%U A333076 48,129624,124224,61560,19312,4168,840,64,16,0,8,225200,210608,107552,32768
%N A333076 Irregular table read by rows: Take an octagon with all diagonals drawn, as in A333075. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.
%C A333076 See the links in A333075 for images of the octagons.
%H A333076 Lars Blomberg, <a href="/A333076/b333076.txt">Table of n, a(n) for n = 1..207</a>
%e A333076 An octagon with no other points along its edges, n = 1, contains 56 triangles, 24 quadrilaterals and no other n-gons, so the first row is [56,24]. An octagon with 1 point dividing its edges, n = 2, contains 800 triangles, 608 quadrilaterals, 64 pentagons, 16 hexagons and no other n-gons, so the second row is [800,608,64,16].
%e A333076 Table begins:
%e A333076 56,24;
%e A333076 800,608,64,16;
%e A333076 4136,3400,1272,464,40;
%e A333076 13840,10800,5296,1264,288,64;
%e A333076 33160,30048,14744,4456,840,152,32;
%e A333076 70832,62208,30848,8656,1936,288,48;
%e A333076 The rows sums are A333075.
%Y A333076 Cf. A333075 (regions), A333109 (vertices), A333110 (edges), A331931, A331906, A007678, A092867, A331452.
%K A333076 nonn,tabf
%O A333076 1,1
%A A333076 _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 07 2020
%E A333076 a(32) and beyond from _Lars Blomberg_, May 14 2020