A095240 Variant of A095236, where first two people choose payphones at the ends.

1, 2, 2, 4, 4, 16, 32, 48, 96, 384, 3072, 9216, 36864, 46080, 184320, 483840, 3870720, 7741440, 82575360, 743178240, 23781703680, 59454259200, 475634073600, 2497078886400, 39953262182400, 22473709977600, 85614133248000

Offset

1,2

Comments

A non-monotonic sequence: a(25) > a(26).

a(n) > a(n+1) for n = 25, 33, 49, 57, 65, 81, 97, 98, 113, 129, 130, 131, 145, 161, 162, 177, 193, 194, 195, 197, ... - Max Alekseyev, Mar 14 2019

Links

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

Simon Wundling, About a combinatorial problem with n seats and n people, arXiv:2303.18175 [math.CO], 2023. (German)

Formula

For n>1, a(n) = A095239(n-1)/(n-1) * 2. - Max Alekseyev, Mar 14 2019

For n>1, a(n) = 2 * Product_{j=1..n-1} 2^(d(n,j)) * (d(n,j))! * (b(n,j) - d(n,j))! (See A095236 for definition and calculation of b(n,j) and d(n,j)). - Simon Wundling, May 21 2023

Example

For example, in a 6-pay-phone situation, person A must pick either pay-phone 1 or pay-phone 6.

Crossrefs

Cf. A095236, A095239.

Sequence in context: A066781 A112869 A086117 * A110428 A076928 A286737

Adjacent sequences: A095237 A095238 A095239 * A095241 A095242 A095243

Keyword

nonn

Author

Matthew Vandermast, Jul 03 2004

Extensions

Edited by Max Alekseyev, Mar 14 2019

Status

approved