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A221720
An avoidance sequence for a pair of tree patterns that is not the avoidance sequence for any set of permutations.
1
1, 1, 2, 5, 12, 26, 49, 83, 129, 187, 257, 339, 433, 539, 657, 787, 929, 1083, 1249, 1427, 1617, 1819, 2033, 2259, 2497, 2747, 3009, 3283, 3569, 3867, 4177, 4499, 4833, 5179, 5537, 5907, 6289, 6683, 7089, 7507, 7937, 8379, 8833, 9299, 9777, 10267, 10769, 11283, 11809, 12347
OFFSET
1,3
LINKS
Dairyko, Michael; Tyner, Samantha; Pudwell, Lara; Wynn, Casey. Non-contiguous pattern avoidance in binary trees. Electron. J. Combin. 19 (2012), no. 3, Paper 22, 21 pp. MR2967227.
M. Dairyko, S. Tyner, L. Pudwell and C. Wynn, Non-contiguous pattern avoidance in binary trees, 2012, arXiv:1203.0795 [math.CO], p. 17 (Class B).
FORMULA
G.f. x*(1-2*x+2*x^2+x^3+2*x^4+3*x^5+2*x^6+2*x^7+x^8)/(1-x)^3.
a(n) = 6*n^2 - 56*n + 147 for n>6. [Bruno Berselli, Feb 05 2013]
MATHEMATICA
CoefficientList[Series[(1 - 2 x + 2 x^2 + x^3 + 2 x^4 + 3 x^5 + 2 x^6 + 2 x^7 + x^8) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)
LinearRecurrence[{3, -3, 1}, {1, 1, 2, 5, 12, 26, 49, 83, 129}, 50] (* Harvey P. Dale, Sep 04 2021 *)
CROSSREFS
Sequence in context: A287141 A214610 A338792 * A258099 A132977 A027927
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 01 2013
STATUS
approved