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A332427 Irregular table read by rows: Take a nonagon with all diagonals drawn, as in A332421. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

%I A332427 #26 Jan 01 2024 22:47:11
%S A332427 90,36,18,9,0,0,1,1332,918,414,90,6525,6453,2529,1071,171,90,10,9,
%T A332427 22248,18882,10368,2988,486,108,18,54558,50985,24750,9387,2034,531,36,
%U A332427 27,9,0,0,0,0,0,0,1,113958,107676,54558,17820,3672,612,36,18
%N A332427 Irregular table read by rows: Take a nonagon with all diagonals drawn, as in A332421. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.
%C A332427 See the links in A332421 for images of the nonagons.
%H A332427 Lars Blomberg, <a href="/A332427/b332427.txt">Table of n, a(n) for n = 1..241</a> (the first 23 rows)
%e A332427 A nonagon with no other points along its edges, n = 1, contains 90 triangles, 36 quadrilaterals, 18 pentagons, 9 hexagons, 1 nonagon and no other n-gons, so the first row is [90,36,18,9,0,0,1]. A nonagon with 1 point dividing its edges, n = 2, contains 1332 triangles, 918 quadrilaterals, 414 pentagons, 90 hexagons and no other n-gons, so the second row is [1332,918,414,90].
%e A332427 Table begins:
%e A332427 90,36,18,9,0,0,1;
%e A332427 1332,918,414,90;
%e A332427 6525,6453,2529,1071,171,90,10,9;
%e A332427 22248,18882,10368,2988,486,108,18;
%e A332427 54558,50985,24750,9387,2034,531,36,27,9,0,0,0,0,0,0,1;
%e A332427 113958,107676,54558,17820,3672,612,36,18;
%e A332427 210591,208089,105417,34407,7560,1737,307,45,0,9;
%e A332427 The row sums are A332421.
%Y A332427 Cf. A332421 (regions), A332428 (vertices), A332429 (edges), A007678, A092867, A331452, A331929.
%K A332427 nonn,tabf
%O A332427 1,1
%A A332427 _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 09 2020
%E A332427 a(36) and beyond from _Lars Blomberg_, May 16 2020