WILFPLUS Example:
Freely braided permutations

The freely braided permutations, introduced by Richard M. Green and Jozsef Losonczy in their article Freely braided elements in Coxeter groups , are the permutations that avoid 3421, 4231, 4312, and 4321. They were first counted by Toufik Mansour in On an open problem of Green and Losonczy: exact enumeration of freely braided permutations , who showed that their generating function is

The first few terms of the sequence are

1, 2, 6, 20, 71, 260, 971, 3674, 14032, 53968, 208692, 810492, 3158760, 12346628, 48377494, 189952216, 747180999, 2943648824, 11612917815, 45869337526, 181372345723, 717856746216, 2843678131629, 11273602645942, 44725291921541, 177551518494116, 705264937798343, 2802952203816934, 11145403903727517, 44337984726749664.

(This is sequence A108600 in the On-Line Encyclopedia of Integer Sequences.)

WILFPLUS finds the following enumeration scheme for this class.

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