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Triangle read by rows: T(n,k) = number of nonequivalent dissections of an n-gon into k polygons by nonintersecting diagonals up to rotation.
5

%I #10 Jan 14 2018 18:18:55

%S 1,1,1,1,1,1,1,2,4,4,1,2,8,12,6,1,3,16,40,43,19,1,3,25,93,165,143,49,

%T 1,4,40,197,505,712,504,150,1,4,56,364,1274,2548,2912,1768,442,1,5,80,

%U 646,2878,7672,12400,11976,6310,1424,1,5,105,1050,5880,19992,42840,58140,48450,22610,4522

%N Triangle read by rows: T(n,k) = number of nonequivalent dissections of an n-gon into k polygons by nonintersecting diagonals up to rotation.

%H Andrew Howroyd, <a href="/A295633/b295633.txt">Table of n, a(n) for n = 3..1277</a>

%e Triangle begins: (n >= 3, k >= 1)

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 2, 4, 4;

%e 1, 2, 8, 12, 6;

%e 1, 3, 16, 40, 43, 19;

%e 1, 3, 25, 93, 165, 143, 49;

%e 1, 4, 40, 197, 505, 712, 504, 150;

%e 1, 4, 56, 364, 1274, 2548, 2912, 1768, 442;

%e ...

%o (PARI) \\ See A295495 for DissectionsModCyclic()

%o T=DissectionsModCyclic(apply(i->y, [1..12]));

%o for(n=3, #T, for(k=1, n-2, print1(polcoeff(T[n], k), ", ")); print)

%Y Row sums are A003455.

%Y Column k=3 is A003451.

%Y Diagonals include A001683, A220881, A003445, A220882.

%Y Cf. A295224, A295495, A295634.

%K nonn,tabl

%O 3,8

%A _Andrew Howroyd_, Nov 24 2017