A362192 A variant of payphone permutations: given a circular booth with n payphones, one of which is already occupied, a(n) is the number ways for n-1 people to choose the payphones in order, where each person chooses an unoccupied payphone such that the closest occupied payphone is as distant as possible.

1, 1, 2, 2, 12, 24, 48, 48, 960, 5760, 20160, 80640, 322560, 645120, 967680, 1935360, 139345920, 2786918400, 30656102400, 367873228800, 2391175987200, 11158821273600, 62768369664000, 1004293914624000, 8034351316992000, 32137405267968000, 96412215803904000, 385648863215616000, 964122158039040000, 1928244316078080000

Offset

1,3

Comments

Provides the same counts as A361296, but up to a choice for the first payphone.

Links

Max Alekseyev, Table of n, a(n) for n = 1..100

Max A. Alekseyev, Enumeration of Payphone Permutations, arXiv:2304.04324 [math.CO], 2023.

Formula

a(n) = A361296(n) / n.

Crossrefs

Cf. A095236, A095239, A095240, A095912, A358056, A361294, A361295, A361296.

Sequence in context: A369086 A355871 A164961 * A122007 A365643 A137782

Adjacent sequences: A362189 A362190 A362191 * A362193 A362194 A362195

Keyword

nonn

Author

Max Alekseyev, Apr 10 2023

Status

approved