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A295634 Triangle read by rows: T(n,k) = number of nonequivalent dissections of an n-gon into k polygons by nonintersecting diagonals up to rotation and reflection. 6

%I #9 Jan 15 2018 03:09:33

%S 1,1,1,1,1,1,1,2,3,3,1,2,6,7,4,1,3,11,24,24,12,1,3,17,51,89,74,27,1,4,

%T 26,109,265,371,259,82,1,4,36,194,660,1291,1478,891,228,1,5,50,345,

%U 1477,3891,6249,6044,3176,733,1,5,65,550,3000,10061,21524,29133,24302,11326,2282

%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 and reflection.

%H Andrew Howroyd, <a href="/A295634/b295634.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, 3, 3;

%e 1, 2, 6, 7, 4;

%e 1, 3, 11, 24, 24, 12;

%e 1, 3, 17, 51, 89, 74, 27;

%e 1, 4, 26, 109, 265, 371, 259, 82;

%e 1, 4, 36, 194, 660, 1291, 1478, 891, 228;

%e ...

%o (PARI) \\ See A295419 for DissectionsModDihedral()

%o T=DissectionsModDihedral(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 A001004.

%Y Column k=3 is A003453.

%Y Diagonals include A000207, A003449, A003450.

%Y Cf. A295260, A295419, A295633.

%K nonn,tabl

%O 3,8

%A _Andrew Howroyd_, Nov 24 2017

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Last modified March 29 09:14 EDT 2024. Contains 371268 sequences. (Running on oeis4.)