A334063 Triangle read by rows: T(n,k) is the number of non-crossing set partitions of {1..5n} into n sets of 5 with k of the sets being a contiguous set of elements.

1, 4, 1, 16, 18, 1, 64, 168, 52, 1, 256, 1216, 936, 121, 1, 1024, 7680, 11040, 3760, 246, 1, 4096, 44544, 103040, 67480, 12264, 455, 1, 16384, 243712, 827904, 888160, 318976, 34524, 784, 1, 65536, 1277952, 5992448, 9554944, 5716704, 1254512, 86980, 1278, 1

Offset

1,2

Comments

T(n,k) is also the number of non-crossing configurations with exactly k polyomino matchings in a generalized game of memory played on the path of length 5n, see [Young].

For the case of partitions of {1..4n} into sets of 4, see A334062.

For the case of partitions of {1..3n} into sets of 3, see A091320.

For the case of partitions of {1..2n} into sets of 2, see A001263.

Links

Table of n, a(n) for n=1..45.

Donovan Young, Linear k-Chord Diagrams, arXiv:2004.06921 [math.CO], 2020.

Formula

G.f.: G(t, z) satisfies z*G^5 - (1 + z - t*z)*G + 1 = 0.

Example

Triangle starts:
     1;
     4,    1;
    16,   18,     1;
    64,  168,    52,    1;
   256, 1216,   936,  121,   1;
  1024, 7680, 11040, 3760, 246,  1;
  ...
For n = 2 and k = 1 the configurations are (1,7,8,9,10), (2,3,4,5,6), (1,2,8,9,10),(3,4,5,6,7), (1,2,3,9,10), (4,5,6,7,8) and (1,2,3,4,10), (5,6,7,8,9); hence T(2,1) = 4.

Crossrefs

Row sums are A002294.

Cf. A001263, A091320, A334062.

Sequence in context: A269698 A059991 A002568 * A111661 A072651 A209411

Adjacent sequences: A334060 A334061 A334062 * A334064 A334065 A334066

Keyword

nonn,tabl

Author

Donovan Young, May 28 2020

Status

approved