A209629 The number of partitions of the set [n] where each element can be colored 1 or 2 avoiding the patterns 1^12^2 and 1^22^1 in the pattern sense.

2, 6, 16, 44, 134, 468, 1880, 8534, 42804, 232972, 1359186, 8431288, 55297064, 381815026, 2765949856, 20960349828, 165729870678, 1364153874460, 11665484934400, 103448317519318, 949739634410652, 9013431481088948, 88304011718557298, 891917738606387792

Offset: 1

Author

Adam Goyt, Mar 13 2012

Keywords

• nonn

Comments

A partition of the set [n] is a family nonempty disjoint sets whose union is [n]. The blocks are written in order of increasing minima. A partition of the set [n] can be written as a word p=p_1p_2...p_n where p_i=j if element i is in block j. A partition q=q_1q_2...q_n contains partition p=p_1p_2...p_k if there is a subword q_{i_1}q_{i_2}...q_{i_k} such that q_{i_a}

Examples

			For n=2 the a(2)=6 solutions are 1^11^1, 1^11^2, 1^21^1, 1^21^2, 1^12^1, 1^22^2.
		

Links

• Adam M. Goyt and Lara K. Pudwell, Avoiding colored partitions of two elements in the pattern sense, arXiv preprint arXiv:1203.3786, 2012. - From _N. J. A. Sloane_, Sep 17 2012

Formula

a(n) = 2^n + 2*(B(n)-1), where B(n) is the n-th Bell number.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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