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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

%I

%S 1,4,1,16,18,1,64,168,52,1,256,1216,936,121,1,1024,7680,11040,3760,

%T 246,1,4096,44544,103040,67480,12264,455,1,16384,243712,827904,888160,

%U 318976,34524,784,1,65536,1277952,5992448,9554944,5716704,1254512,86980,1278,1

%N 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.

%C 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].

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

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

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

%H Donovan Young, <a href="https://arxiv.org/abs/2004.06921">Polyomino matchings in generalised games of memory and linear k-chord diagrams</a>, arXiv:2004.06921 [math.CO], 2020.

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

%e Triangle starts:

%e 1;

%e 4, 1;

%e 16, 18, 1;

%e 64, 168, 52, 1;

%e 256, 1216, 936, 121, 1;

%e 1024, 7680, 11040, 3760, 246, 1;

%e ...

%e 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.

%Y Row sums are A002294.

%Y Cf. A001263, A091320, A334062.

%K nonn,tabl

%O 1,2

%A _Donovan Young_, May 28 2020

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Last modified September 24 07:01 EDT 2020. Contains 337317 sequences. (Running on oeis4.)