A394238 Number of circular parking functions of length n avoiding the pattern 111.

1, 2, 5, 28, 204, 2000, 24030, 344652, 5740560, 109023264, 2326287600, 55117624320, 1436196484800, 40826537706240, 1257537996514800, 41726938979325600, 1484001670159008000, 56319120817785745920, 2271900191107266720000, 97080540724816485258240

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Lara Pudwell, Pattern avoidance in cyclic parking functions, 2025.

Lara Pudwell, Pattern Avoidance in Circular Parking Functions, Valparaiso Univ. (2026). See p. 6 (Table 2).

Formula

If n is odd, a(n) = A036774(n+1)/(n*(n+1)).

If n is even, a(n) = (A036774(n+1)+(n+1)!/(n/2+1)!)/(n*(n+1)).

Example

For n=4, the a(4)=28 parking functions are 1122, 1123, 1124, 1132, 1133, 1134, 1142, 1143, 1212, 1213, 1214, 1223, 1224, 1232, 1233, 1234, 1242, 1243, 1313, 1314, 1322, 1323, 1324, 1332, 1342, 1422, 1423, 1432.

Crossrefs

Cf. A019536, A036774, A121774, A171005, A213937, A393352, A394236, A394237.

Sequence in context: A072371 A019043 A009635 * A216401 A342288 A324264

Adjacent sequences: A394235 A394236 A394237 * A394239 A394240 A394241

Keyword

nonn

Author

Lara Pudwell, Mar 13 2026

Status

approved