

A334063


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


1



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
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OFFSET

1,2


COMMENTS

T(n,k) is also the number of noncrossing 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, Polyomino matchings in generalised games of memory and linear kchord 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 * A334065 A334066 A334067


KEYWORD

nonn,tabl


AUTHOR

Donovan Young, May 28 2020


STATUS

approved



