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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
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 (list; table; graph; refs; listen; history; text; internal format)
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, Polyomino matchings in generalised games of memory and 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 * A334065 A334066 A334067

KEYWORD

nonn,tabl

AUTHOR

Donovan Young, May 28 2020

STATUS

approved

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Last modified August 9 04:39 EDT 2020. Contains 336319 sequences. (Running on oeis4.)