A221720 An avoidance sequence for a pair of tree patterns that is not the avoidance sequence for any set of permutations.

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

Adjacent sequences: A221717 A221718 A221719 * A221721 A221722 A221723

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 01 2013

Status

approved