cp's OEIS Frontend

A332417 Irregular table read by rows: Take a decagon with all diagonals drawn, as in A333139. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

%I A332417 #24 Oct 14 2020 23:15:09
%S A332417 120,90,10,2040,1580,460,140,10860,8570,4170,1380,210,20,10,34360,
%T A332417 30420,14240,4020,1120,100,20,85600,76920,38610,13360,2650,550,110,
%U A332417 176760,166400,82560,24500,5500,760,140,20,327550,320520,159860,51610,10960,2250,300,30,0,10
%N A332417 Irregular table read by rows: Take a decagon with all diagonals drawn, as in A333139. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.
%C A332417 See the links in A333139 for images of the decagons.
%H A332417 Lars Blomberg, <a href="/A332417/b332417.txt">Table of n, a(n) for n = 1..181</a> (the first 21 rows)
%e A332417 A decagon with no other points along its edges, n = 1, contains 120 triangles, 90 quadrilaterals, 10 pentagons and no other n-gons, so the first row is [120, 90, 10]. A decagon with 1 point dividing its edges, n = 2, contains 2040 triangles, 1580 quadrilaterals, 460 pentagons, 140 hexagons and no other n-gons, so the second row is [2040,1580,460,140].
%e A332417 Table begins:
%e A332417 120, 90, 10;
%e A332417 2040,1580,460,140;
%e A332417 10860,8570,4170,1380,210,20,10;
%e A332417 34360,30420,14240,4020,1120,100,20;
%e A332417 85600,76920,38610,13360,2650,550,110;
%e A332417 176760, 166400, 82560, 24500, 5500, 760, 140, 20;
%e A332417 327550, 320520, 159860, 51610, 10960, 2250, 300, 30, 0, 10;
%e A332417 565060, 549520, 277360, 86540, 18960, 3560, 480, 20, 20;
%e A332417 910920, 891290, 447790, 147300, 32180, 5640, 720, 130, 40, 10;
%e A332417 The row sums are A333139.
%Y A332417 Cf. A333139 (regions), A332418 (vertices), A332419 (edges), A007678, A092867, A331452, A331929.
%K A332417 nonn,tabf
%O A332417 1,1
%A A332417 _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 09 2020
%E A332417 a(29) and beyond from _Lars Blomberg_, May 18 2020