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A192008 Modified linear pay-phone sequence: number of ways to occupy n pay-phones in a row one-by-one, each time picking a phone adjacent to the smallest number of previously occupied phones. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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

EXAMPLE

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).

PROG

(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

CROSSREFS

Cf. A095236, A192009, A276657.

Sequence in context: A271216 A102000 A165904 * A074406 A186340 A228920

Adjacent sequences:  A192005 A192006 A192007 * A192009 A192010 A192011

KEYWORD

nonn

AUTHOR

Jens Voß, Jun 21 2011

EXTENSIONS

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

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

STATUS

approved

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Last modified March 28 12:08 EDT 2017. Contains 284186 sequences.