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A363809
Number of permutations of [n] that avoid the patterns 2-41-3, 3-14-2, and 2-1-3-5-4.
4
1, 1, 2, 6, 22, 89, 378, 1647, 7286, 32574, 146866, 667088, 3050619, 14039075, 64992280, 302546718, 1415691181, 6656285609, 31436228056, 149079962872, 709680131574, 3390269807364, 16248661836019, 78109838535141, 376531187219762, 1819760165454501
OFFSET
0,3
COMMENTS
Equivalently, for n>0, the number of separable permutations of [n] that avoid 2-1-3-5-4.
The number of guillotine rectangulations (with respect to the weak equivalence) that avoid the geometric pattern "7". See the Merino and Mütze reference, Table 3, entry "12347".
REFERENCES
Andrei Asinowski and Cyril Banderier. Geometry meets generating functions: Rectangulations and permutations (2023).
LINKS
Andrei Asinowski and Cyril Banderier, From geometry to generating functions: rectangulations and permutations, arXiv:2401.05558 [cs.DM], 2024. See page 2.
Arturo Merino and Torsten Mütze. Combinatorial generation via permutation languages. III. Rectangulations. Discrete & Computational Geometry, 70 (2023), 51-122. Preprint: arXiv:2103.09333 [math.CO], 2021.
FORMULA
The generating function F=F(x) satisfies the equation x^4*(x - 2)^2*F^4 + x*(x - 2)*(4*x^3 - 7*x^2 + 6*x - 1)*F^3 + (2*x^4 - x^3 - 2*x^2 + 5*x - 1)*F^2 - (4*x^3 - 7*x^2 + 6*x - 1)*F + x^2 = 0.
CROSSREFS
Other entries including the patterns 1, 2, 3, 4 in the Merino and Mütze reference: A006318, A106228, A078482, A033321, A363810, A363811, A363812, A363813, A006012.
Sequence in context: A150267 A271388 A165540 * A111053 A165541 A165542
KEYWORD
nonn
AUTHOR
Andrei Asinowski, Jun 23 2023
STATUS
approved