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.

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, 26, 109, 265, 371, 259, 82, 1, 4, 36, 194, 660, 1291, 1478, 891, 228, 1, 5, 50, 345, 1477, 3891, 6249, 6044, 3176, 733, 1, 5, 65, 550, 3000, 10061, 21524, 29133, 24302, 11326, 2282

Offset

3,8

Links

Andrew Howroyd, Table of n, a(n) for n = 3..1277

Example

Triangle begins: (n >= 3, k >= 1)
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, 26, 109, 265,  371,  259,  82;
1, 4, 36, 194, 660, 1291, 1478, 891, 228;
...

Prog

(PARI) \\ See A295419 for DissectionsModDihedral()
T=DissectionsModDihedral(apply(i->y, [1..12]));
for(n=3, #T, for(k=1, n-2, print1(polcoeff(T[n], k), ", ")); print)

Crossrefs

Row sums are A001004.

Column k=3 is A003453.

Diagonals include A000207, A003449, A003450.

Cf. A295260, A295419, A295633.

Sequence in context: A106595 A181608 A272873 * A317665 A329315 A109199

Adjacent sequences: A295631 A295632 A295633 * A295635 A295636 A295637

Keyword

nonn,tabl

Author

Andrew Howroyd, Nov 24 2017

Status

approved