A295633 Triangle read by rows: T(n,k) = number of nonequivalent dissections of an n-gon into k polygons by nonintersecting diagonals up to rotation.

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, 1, 4, 40, 197, 505, 712, 504, 150, 1, 4, 56, 364, 1274, 2548, 2912, 1768, 442, 1, 5, 80, 646, 2878, 7672, 12400, 11976, 6310, 1424, 1, 5, 105, 1050, 5880, 19992, 42840, 58140, 48450, 22610, 4522

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,  4,   4;
1, 2,  8,  12,    6;
1, 3, 16,  40,   43,   19;
1, 3, 25,  93,  165,  143,   49;
1, 4, 40, 197,  505,  712,  504,  150;
1, 4, 56, 364, 1274, 2548, 2912, 1768, 442;
...

Prog

(PARI) \\ See A295495 for DissectionsModCyclic()
T=DissectionsModCyclic(apply(i->y, [1..12]));
for(n=3, #T, for(k=1, n-2, print1(polcoeff(T[n], k), ", ")); print)

Crossrefs

Row sums are A003455.

Column k=3 is A003451.

Diagonals include A001683, A220881, A003445, A220882.

Cf. A295224, A295495, A295634.

Sequence in context: A258712 A238094 A140734 * A159778 A243278 A378978

Adjacent sequences: A295630 A295631 A295632 * A295634 A295635 A295636

Keyword

nonn,tabl

Author

Andrew Howroyd, Nov 24 2017

Status

approved