A229158 Triangle T(n,k) read by rows: T(n,k) = number of permutations on 123...n with exactly two abc patterns and no aj pattern with j<=k, for n>=0, 0<=k<=n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 1, 0, 0, 24, 24, 12, 2, 0, 0, 133, 133, 74, 23, 3, 0, 0, 635, 635, 371, 141, 36, 4, 0, 0, 2807, 2807, 1688, 709, 227, 51, 5, 0, 0, 11864, 11864, 7276, 3248, 1168, 334, 68, 6, 0, 0, 48756, 48756, 30340, 14121, 5459, 1771, 464, 87, 7, 0, 0

Offset: 0

Author

N. J. A. Sloane, Sep 15 2013

Keywords

• nonn
• tabl

Comments

See Noonan-Zeilberger for precise definition.

Examples

			Triangle begins:
0,
0,0,
0,0,0,
0,0,0,0,
3,3,1,0,0,
24,24,12,2,0,0,
133,133,74,23,3,0,0,
635,635,371,141,36,4,0,0,
2807,2807,1688,709,227,51,5,0,0,
11864,11864,7276,3248,1168,334,68,6,0,0,
48756,48756,30340,14121,5459,1771,464,87,7,0,0
...
		

Links

• J. Noonan and D. Zeilberger, [math/9808080] The Enumeration of Permutations With a Prescribed Number of ``Forbidden'' Patterns. Also Adv. in Appl. Math. 17 (1996), no. 4, 381--407. MR1422065 (97j:05003).

Crossrefs

Cf. A228708, A001089.