<s>
In	O
the	O
study	O
of	O
permutation	B-Algorithm
patterns	I-Algorithm
,	O
there	O
has	O
been	O
considerable	O
interest	O
in	O
enumerating	O
specific	O
permutation	O
classes	O
,	O
especially	O
those	O
with	O
relatively	O
few	O
basis	O
elements	O
.	O
</s>
<s>
2143	B-Algorithm
1	O
,	O
2	O
,	O
6	O
,	O
23	O
,	O
103	O
,	O
513	O
,	O
2761	O
,	O
15767	O
,	O
...	O
holonomic	O
(	O
nonalgebraic	O
)	O
g.f.	O
1324	O
1	O
,	O
2	O
,	O
6	O
,	O
23	O
,	O
103	O
,	O
513	O
,	O
2762	O
,	O
15793	O
,	O
...	O
</s>
<s>
231	B-Algorithm
,	O
312	O
1	O
,	O
2	O
,	O
4	O
,	O
8	O
,	O
16	O
,	O
32	O
,	O
64	O
,	O
128	O
,	O
...	O
rational	O
g.f.	O
,	O
</s>
<s>
B	O
sequence	O
enumerating	O
Avn(B )	O
OEIS	O
type	O
of	O
sequence	O
321	O
,	O
1234	O
1	O
,	O
2	O
,	O
5	O
,	O
13	O
,	O
25	O
,	O
25	O
,	O
0	O
,	O
0	O
,	O
...	O
n/a	O
finite	O
321	O
,	O
2134	O
1	O
,	O
2	O
,	O
5	O
,	O
13	O
,	O
30	O
,	O
61	O
,	O
112	O
,	O
190	O
,	O
...	O
polynomial	O
132	O
,	O
4321	O
1	O
,	O
2	O
,	O
5	O
,	O
13	O
,	O
31	O
,	O
66	O
,	O
127	O
,	O
225	O
,	O
...	O
polynomial	O
321	O
,	O
1324	O
1	O
,	O
2	O
,	O
5	O
,	O
13	O
,	O
32	O
,	O
72	O
,	O
148	O
,	O
281	O
,	O
...	O
polynomial	O
321	O
,	O
1342	O
1	O
,	O
2	O
,	O
5	O
,	O
13	O
,	O
32	O
,	O
74	O
,	O
163	O
,	O
347	O
,	O
...	O
rational	O
g.f.	O
321	O
,	O
2143	B-Algorithm
1	O
,	O
2	O
,	O
5	O
,	O
13	O
,	O
33	O
,	O
80	O
,	O
185	O
,	O
411	O
,	O
...	O
rational	O
g.f.	O
</s>
<s>
B	O
sequence	O
enumerating	O
Avn(B )	O
OEIS	O
type	O
of	O
sequence	O
exact	O
enumeration	O
reference	O
4321	O
,	O
1234	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
306	O
,	O
882	O
,	O
1764	O
,	O
...	O
finite	O
Erdős	O
–	O
Szekeres	O
theorem	O
4312	O
,	O
1234	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
321	O
,	O
1085	O
,	O
3266	O
,	O
...	O
polynomial	O
4321	O
,	O
3124	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
330	O
,	O
1198	O
,	O
4087	O
,	O
...	O
rational	O
g.f.	O
4312	O
,	O
2134	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
330	O
,	O
1206	O
,	O
4174	O
,	O
...	O
rational	O
g.f.	O
4321	O
,	O
1324	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
332	O
,	O
1217	O
,	O
4140	O
,	O
...	O
polynomial	O
4321	O
,	O
2143	B-Algorithm
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
333	O
,	O
1235	O
,	O
4339	O
,	O
...	O
rational	O
g.f.	O
4312	O
,	O
1324	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
335	O
,	O
1266	O
,	O
4598	O
,	O
...	O
rational	O
g.f.	O
4231	O
,	O
2143	B-Algorithm
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
335	O
,	O
1271	O
,	O
4680	O
,	O
...	O
rational	O
g.f.	O
4231	O
,	O
1324	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
336	O
,	O
1282	O
,	O
4758	O
,	O
...	O
rational	O
g.f.	O
4213	O
,	O
2341	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
336	O
,	O
1290	O
,	O
4870	O
,	O
...	O
rational	O
g.f.	O
4312	O
,	O
2143	B-Algorithm
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
337	O
,	O
1295	O
,	O
4854	O
,	O
...	O
rational	O
g.f.	O
4213	O
,	O
1243	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
337	O
,	O
1299	O
,	O
4910	O
,	O
...	O
rational	O
g.f.	O
4321	O
,	O
3142	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
338	O
,	O
1314	O
,	O
5046	O
,	O
...	O
rational	O
g.f.	O
4213	O
,	O
1342	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
338	O
,	O
1318	O
,	O
5106	O
,	O
...	O
rational	O
g.f.	O
4312	O
,	O
2341	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
338	O
,	O
1318	O
,	O
5110	O
,	O
...	O
rational	O
g.f.	O
3412	O
,	O
2143	B-Algorithm
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
340	O
,	O
1340	O
,	O
5254	O
,	O
...	O
algebraic	O
(	O
nonrational	O
)	O
g.f.	O
</s>
<s>
4123	O
,	O
2143	B-Algorithm
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
86	O
,	O
342	O
,	O
1366	O
,	O
5462	O
,	O
...	O
rational	O
g.f.	O
4123	O
,	O
2341	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
87	O
,	O
348	O
,	O
1374	O
,	O
5335	O
,	O
...	O
algebraic	O
(	O
nonrational	O
)	O
g.f.	O
4231	O
,	O
3214	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
87	O
,	O
352	O
,	O
1428	O
,	O
5768	O
,	O
...	O
algebraic	O
(	O
nonrational	O
)	O
g.f.	O
4213	O
,	O
1432	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
87	O
,	O
352	O
,	O
1434	O
,	O
5861	O
,	O
...	O
algebraic	O
(	O
nonrational	O
)	O
g.f.	O
</s>
<s>
4213	O
,	O
2314	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
88	O
,	O
366	O
,	O
1552	O
,	O
6652	O
,	O
...	O
algebraic	O
(	O
nonrational	O
)	O
g.f.	O
4213	O
,	O
2143	B-Algorithm
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
88	O
,	O
366	O
,	O
1556	O
,	O
6720	O
,	O
...	O
algebraic	O
(	O
nonrational	O
)	O
g.f.	O
4312	O
,	O
3142	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
88	O
,	O
367	O
,	O
1568	O
,	O
6810	O
,	O
...	O
algebraic	O
(	O
nonrational	O
)	O
g.f.	O
4213	O
,	O
3421	O
1	O
,	O
2	O
,	O
6	O
,	O
22	O
,	O
88	O
,	O
367	O
,	O
1571	O
,	O
6861	O
,	O
...	O
algebraic	O
(	O
nonrational	O
)	O
g.f.	O
</s>
