

A334062


Triangle read by rows: T(n,k) is the number of noncrossing set partitions of {1..4n} into n sets of 4 with k of the sets being a contiguous set of elements.


1



1, 3, 1, 9, 12, 1, 27, 81, 31, 1, 81, 432, 390, 65, 1, 243, 2025, 3330, 1365, 120, 1, 729, 8748, 22815, 17415, 3909, 203, 1, 2187, 35721, 135513, 166320, 70938, 9730, 322, 1, 6561, 139968, 728028, 1312038, 911358, 242004, 21816, 486, 1, 19683, 531441, 3630420, 9032310, 9294264, 4067658, 722316, 45090, 705, 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 4n, see [Young].
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..55.
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^4  (1 + z  t*z)*G + 1 = 0.


EXAMPLE

Triangle starts:
1;
3, 1;
9, 12, 1;
27, 81, 31, 1;
81, 432, 390, 65, 1;
243, 2025, 3330, 1365, 120, 1;
...
For n=2 and k=1 the configurations are (1,6,7,8),(2,3,4,5), (1,2,7,8),(3,4,5,6), and (1,2,3,8),(4,5,6,7); hence T(2,1) = 3.


CROSSREFS

Row sums are A002293.
Column 2 is A069996.
Cf. A001263, A091320, A334063.
Sequence in context: A260285 A242499 A173020 * A157383 A232598 A174510
Adjacent sequences: A334059 A334060 A334061 * A334063 A334064 A334065


KEYWORD

nonn,tabl


AUTHOR

Donovan Young, May 28 2020


STATUS

approved



