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 A334062 Triangle read by rows: T(n,k) is the number of non-crossing 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 (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 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 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^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

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Last modified September 24 07:28 EDT 2020. Contains 337317 sequences. (Running on oeis4.)