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.

1, 2, 4, 8, 32, 96, 456, 2016, 11232, 61632, 419328, 2695680, 21358080, 161049600, 1433894400, 12429158400, 123511910400, 1202903654400, 13229501644800, 143113833676800, 1722282128179200, 20516624400384000, 268083853148160000, 3485314242772992000, 49167975665958912000

Offset: 1

Author

Jens Voß, Jun 21 2011

Keywords

• nonn

Examples

			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).
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..100
• Project Euler, Comfortable distance (Problem 364).
• Jens Voß, Java class for generating A192008

Crossrefs

Cf. A095236, A192009, A276657.

Programs

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

Formula

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

Extensions

More terms from João Batista Souza de Oliveira, Jul 09 2014

Terms a(20) onward from Max Alekseyev, Sep 11 2016