login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..55.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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