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%I #27 Sep 29 2019 02:52:13
%S 1,2,4,8,32,96,456,2016,11232,61632,419328,2695680,21358080,161049600,
%T 1433894400,12429158400,123511910400,1202903654400,13229501644800,
%U 143113833676800,1722282128179200,20516624400384000,268083853148160000,3485314242772992000,49167975665958912000
%N 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 Max Alekseyev, <a href="/A192008/b192008.txt">Table of n, a(n) for n = 1..100</a>
%H Project Euler, <a href="http://projecteuler.net/problem=364">Comfortable distance</a> (Problem 364).
%H Jens Voß, <a href="/A192008/a192008.java.txt">Java class for generating A192008</a>
%F 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 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 (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 Cf. A095236, A192009, A276657.
%K nonn
%O 1,2
%A _Jens Voß_, Jun 21 2011
%E More terms from _João Batista Souza de Oliveira_, Jul 09 2014
%E Terms a(20) onward from _Max Alekseyev_, Sep 11 2016
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