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A192008
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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.
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3
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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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
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EXAMPLE
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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).
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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