A276657 -id:A276657 - cp's OEIS frontend

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

Jens Voß, Jun 21 2011

nonn

			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).

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

Cf. A095236, A192009, A276657.

{ 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

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

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

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

A192009 Modified cyclic phone booth sequence: number of ways to occupy n labeled phone booths in a circle one by one, each time picking a phone booth adjacent to the smallest number of previously occupied phone booths.

Original entry on oeis.org

1, 2, 6, 8, 40, 168, 504, 3456, 15552, 97920, 620928, 4465152, 31449600, 273369600, 2172096000, 20968243200, 192753561600, 2032260710400, 20942298316800, 243270107136000, 2758764950323200, 34958441123020800, 434690126954496000, 5946571752210432000, 80503989505228800000

Offset: 1

Jens Voß, Jun 21 2011

nonn

			For n=4, the A192009(n) = 6 ways of picking the phone booths are (1, 3, 2, 4), (1, 3, 4, 2), (2, 4, 1, 3), (2, 4, 3, 1), (3, 1, 2, 4), (3, 1, 4, 2), (4, 2, 1, 3), (4, 2, 3, 1).

Max Alekseyev, Table of n, a(n) for n = 1..100

Cf. A095236, A192008, A192009, A276657.

A192009 := proc(n)
    local a,k,m;
    if n = 1 then
        return 1;
    end if;
    a := 0 ;
    for k from 0 to n/3 do
        m := (n-3*k)/2 ;
        if type (m,'integer') then
            a := a+(m+k-1)!*binomial(m+k,m)*2^k*k!*(m+k)! ;
        end if;
    end do:
    a*n ;
end proc:
seq(A192009(n),n=1..20) ; # R. J. Mathar, Sep 17 2016

r[n_] := {ToRules[Reduce[m >= 0 && k >= 0 && 2m+3k == n, {m, k}, Integers] ]}; f[{m_, k_}] := (m+k-1)!*Binomial[m + k, m]*2^k*k!*(m+k)!; a[n_] := n*Total[f /@ ({m, k} /. r[n])]; a[1] = 1; Array[a, 25] (* Jean-François Alcover, Sep 13 2016, after Max Alekseyev *)

{ A192009(n) = my(r,k); if(n==1,return(1)); r=0; forstep(m=lift(Mod(n,3)/2),n\2,3, k=(n-2*m)\3; r+=(m+k-1)!*binomial(m+k,m)*2^k*k!*(m+k)!); r*n; } \\ Max Alekseyev, Sep 11 2016

For n > 1, a(n) = n * Sum (m+k-1)!*binomial(m+k,m)*2^k*k!*(m+k)!, where the sum is taken over nonnegative m,k such that 2*m+3*k = n. - Max Alekseyev, Sep 11 2016

a(n) = n * A276657(n). - Max Alekseyev, Sep 11 2016

Terms a(15) onward from Max Alekseyev, Sep 11 2016

cp's OEIS Frontend

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.

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