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A180349 Gog words avoiding the subpattern 312 0
1, 2, 6, 26, 162, 1450, 18626, 343210, 9069306, 343611106, 18662952122, 1453016097506 (list; graph; refs; listen; history; text; internal format)



Gog words of size n are words of length n in an alphabet

of odd-sized tuples of increasing integers

that satisfy the following conditions:

(1) The length of the word is n,

(2) Each letter in the word has maximum entry at most n,

(3) An integer in an even numbered position in a tuple is repeated in another tuple to its left and to its right in odd numbered positions,

(4) Every repeated integer alternates in odd and even numbered positions in subsequent tuples.

They are in natural bijection with alternating sign matrices.

Further, the integers c, a, b form a 312-subpattern of the Gog word w = x_1 x_2 ... x_n if the following conditions hold

(1) c, a, b appear in odd positions in x_i, x_j , x_k respectively where i<j<k,

(2) b is not in an even position in x_{i+1},..., x_{k-1},

(3) If x_j = (p_1, q_1, . . . , p_{k-1}, q_{k-1}, p_k), either b>p_k or p_l < b < q_l for some l.

(4) a < b < c.


Table of n, a(n) for n=1..12.

Arvind Ayyer, Robert Cori, Dominique Gouyou-Beauchamps,

Monotone triangles and 312 pattern avoidance, arXiv:1101.1666


For n=3, there are 7 gog words - (1)(2)(3), (1)(3)(2), (2)(1)(3), (2)(3)(1), (3)(1)(2), (3)(2)(1) and (2)(123)(2). Of these, all but (3)(1)(2) avoid the subpattern 312.

More complicated examples: 31(234)3 and 25(12356)542 contain the subpattern 312 but 25(12456)532 does not.


Cf. A005130, A000108, A116715, A116722, A116735

Sequence in context: A213430 A103367 A047863 * A141713 A005272 A307082

Adjacent sequences:  A180346 A180347 A180348 * A180350 A180351 A180352




Arvind Ayyer, Jan 18 2011



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Last modified April 18 15:08 EDT 2021. Contains 343089 sequences. (Running on oeis4.)