A224248
Number of permutations in S_n containing exactly one increasing subsequence of length 5.
Original entry on oeis.org
0, 0, 0, 0, 0, 1, 20, 270, 3142, 34291, 364462, 3844051, 40632886, 432715409, 4655417038, 50667480496, 558143676522, 6223527776874, 70228214538096, 801705888742781, 9254554670121572, 107975393459449243, 1272651313142352772, 15145990284267530992
Offset: 0
- B. Nakamura and D. Zeilberger, Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes, Adv. in Appl. Math. 50 (2013), 356-366.
A224249
Number of permutations in S_n containing exactly 2 increasing subsequences of length 4.
Original entry on oeis.org
0, 0, 0, 0, 4, 63, 665, 5982, 49748, 396642, 3089010, 23745117, 181282899, 1379847138, 10496697584, 79928658289, 609847716251, 4665446254886, 35801131210504, 275638351332190, 2129514056354378, 16509890253429971, 128449405928666831, 1002835093225654416, 7856166360951643384
Offset: 1
A224179
Number of permutations of length n containing exactly 1 occurrence of 1243.
Original entry on oeis.org
0, 0, 0, 1, 11, 88, 638, 4478, 31199, 218033, 1535207, 10910759, 78310579, 567588264, 4152765025, 30656248812, 228215224472, 1712296117750, 12941799657414, 98486737654025, 754273093950128, 5811161481943201, 45020589539040033, 350604675228411590, 2743720335733822423
Offset: 1
- Andrew R. Conway and Anthony J. Guttmann, Counting occurrences of patterns in permutations, arXiv:2306.12682 [math.CO], 2023. See pp. 16, 20.
- Brian Nakamura, Approaches for enumerating permutations with a prescribed number of occurrences of patterns, PU. M. A. 24 (2013), 179-194.
- Brian Nakamura, Approaches for enumerating permutations with a prescribed number of occurrences of patterns, arXiv 1301.5080, 2013
A224298
Number of permutations in S_n containing exactly 3 increasing subsequences of length 4.
Original entry on oeis.org
0, 0, 0, 0, 0, 10, 196, 2477, 25886, 244233, 2167834, 18510734, 154082218, 1260811144, 10198142484, 81848366557, 653537296202, 5201485318177, 41321901094750, 327996498249202
Offset: 1
- B. Nakamura and D. Zeilberger, Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes, Adv. in Appl. Math. 50 (2013), 356-366.
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