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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. 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
Project Euler, Comfortable distance (Problem 364).
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
Sequence in context: A102000 A372256 A165904 * A298989 A074406 A186340
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 June 20 08:00 EDT 2024. Contains 373512 sequences. (Running on oeis4.)