cp's OEIS Frontend

A192008 Modified linear phone booth sequence: number of ways to occupy n phone booths in a row, one by one, each time picking a phone booth adjacent to the smallest number of previously occupied phone booths.

%I A192008 #27 Sep 29 2019 02:52:13
%S A192008 1,2,4,8,32,96,456,2016,11232,61632,419328,2695680,21358080,161049600,
%T A192008 1433894400,12429158400,123511910400,1202903654400,13229501644800,
%U A192008 143113833676800,1722282128179200,20516624400384000,268083853148160000,3485314242772992000,49167975665958912000
%N A192008 Modified linear phone booth sequence: number of ways to occupy n phone booths in a row, one by one, each time picking a phone booth adjacent to the smallest number of previously occupied phone booths.
%H A192008 Max Alekseyev, <a href="/A192008/b192008.txt">Table of n, a(n) for n = 1..100</a>
%H A192008 Project Euler, <a href="http://projecteuler.net/problem=364">Comfortable distance</a> (Problem 364).
%H A192008 Jens Voß, <a href="/A192008/a192008.java.txt">Java class for generating A192008</a>
%F A192008 a(n) = Sum (m+k+1)!*binomial(m+k,m)*2^k*(k+v1+v2)!*(m+k)!, where the sum is taken over v1,v2 each from 0 to 1, and over nonnegative m,k such that 2*m+3*k = n-1-v1-v2. - _Max Alekseyev_, Sep 11 2016
%e A192008 For n=4, the A192008(n) = 8 ways of picking the phones are (1, 3, 4, 2), (1, 4, 2, 3), (1, 4, 3, 2), (2, 4, 1, 3), (3, 1, 4, 2), (4, 1, 2, 3), (4, 1, 3, 2), (4, 2, 1, 3).
%o A192008 (PARI) { A192008(n) = my(r,k); r=0; for(v=0,2, forstep(m=lift(Mod(n-1-v,3)/2),(n-1-v)\2,3, k=(n-1-v-2*m)\3; r+=(m+k+1)!*binomial(m+k,m)*2^k*(k+v)!*(m+k)!*(1+(v==1)););); r; } \\ _Max Alekseyev_, Sep 11 2016
%Y A192008 Cf. A095236, A192009, A276657.
%K A192008 nonn
%O A192008 1,2
%A A192008 _Jens Voß_, Jun 21 2011
%E A192008 More terms from _João Batista Souza de Oliveira_, Jul 09 2014
%E A192008 Terms a(20) onward from _Max Alekseyev_, Sep 11 2016