A358056 -id:A358056 - cp's OEIS frontend

A361294 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, and a payphone adjacent to a single occupied payphone is preferred over a payphone sandwiched between two occupied payphones.

1, 1, 2, 2, 8, 16, 24, 48, 192, 1536, 4608, 18432, 23040, 92160, 241920, 1935360, 3870720, 41287680, 371589120, 11890851840, 29727129600, 237817036800, 1248539443200, 19976631091200, 11236854988800, 42807066624000, 176579149824000, 3390319676620800, 6886586843136000

Offset: 1

Max Alekseyev, Apr 10 2023

nonn

Provides the same counts as A095239, but up to a choice for the first payphone.

Max Alekseyev, Table of n, a(n) for n = 1..100
Max A. Alekseyev, Enumeration of Payphone Permutations, arXiv:2304.04324 [math.CO], 2023.

Cf. A095236, A095239, A095240, A095912, A358056, A361295, A361296, A362192.

a(n) = A095239(n) / n = A095240(n+1) / 2.

A361295 A variant of payphone permutations: given a row of n payphones, a(n) is the number ways for n 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, and among the available payphones adjacent to a single occupied payphone the most preferred are payphones at open ends.

Original entry on oeis.org

1, 2, 4, 6, 12, 40, 144, 384, 1008, 6816, 33600, 115200, 783360, 3024000, 16450560, 140636160, 558351360, 2262435840, 29599395840, 180278784000, 2124328550400, 13664957644800, 127667338444800, 852837440716800, 11377123378790400, 116737211695104000, 816490952589312000

Offset: 1

Max Alekseyev, Apr 08 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 1..100
Max A. Alekseyev, Enumeration of Payphone Permutations, arXiv:2304.04324 [math.CO], 2023.

Cf. A358056, A095236, A095239, A095912, A361294, A361296, A362192, A363785.

Definition corrected by Max Alekseyev, Jun 21 2023

A361296 A variant of payphone permutations: given a circular booth with n payphones, a(n) is the number ways for n 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.

Original entry on oeis.org

1, 2, 6, 8, 60, 144, 336, 384, 8640, 57600, 221760, 967680, 4193280, 9031680, 14515200, 30965760, 2368880640, 50164531200, 582465945600, 7357464576000, 50214695731200, 245494068019200, 1443672502272000, 24103053950976000, 200858782924800000, 835572536967168000

Offset: 1

Max Alekseyev, Apr 08 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 1..100
Max A. Alekseyev, Enumeration of Payphone Permutations, arXiv:2304.04324 [math.CO], 2023.

Cf. A095236, A095239, A095912, A358056, A361294, A361295, A362192.

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.

Original entry on oeis.org

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

Max Alekseyev, Apr 10 2023

nonn

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

Max Alekseyev, Table of n, a(n) for n = 1..100
Max A. Alekseyev, Enumeration of Payphone Permutations, arXiv:2304.04324 [math.CO], 2023.

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

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

A363785 A variant of payphone permutations: given a row of n payphones, a(n) is the number ways for n 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, and a payphone adjacent to a single occupied payphone is preferred over a payphone sandwiched between two occupied payphones.

Original entry on oeis.org

1, 2, 4, 6, 16, 28, 120, 264, 576, 2784, 11040, 37440, 204672, 679680, 2511360, 15655680, 52945920, 232796160, 2456801280, 11867627520, 97875025920, 576737280000, 4012233523200, 20013325516800, 215802239385600, 1778700504268800, 9687506721177600, 88613303353344000, 448250987623219200

Offset: 1

Max Alekseyev, Jun 21 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 1..100
Max A. Alekseyev, Enumeration of Payphone Permutations, arXiv:2304.04324 [math.CO], 2023.

Cf. A358056, A095236, A095239, A095912, A361294, A361295, A361296, A362192, A363785.

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A361296 A variant of payphone permutations: given a circular booth with n payphones, a(n) is the number ways for n 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.

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