cp's OEIS Frontend

A276657 Number of ways to occupy n unlabeled phone booths in a circle one by one, each time picking a phone booth adjacent to the smallest number of previously occupied phone booths.

%I A276657 #14 Sep 29 2019 02:37:45
%S A276657 1,1,2,2,8,28,72,432,1728,9792,56448,372096,2419200,19526400,
%T A276657 144806400,1310515200,11338444800,112903372800,1102226227200,
%U A276657 12163505356800,131369759539200,1589020051046400,18899570737152000,247773823008768000,3220159580209152000,45535430530695168000
%N A276657 Number of ways to occupy n unlabeled phone booths in a circle one by one, each time picking a phone booth adjacent to the smallest number of previously occupied phone booths.
%C A276657 Each phone booth has two adjacent ones, each of which may or may not be occupied. So, available phone booths may have from 0 to 2 adjacent ones that are occupied. Each time we pick a phone booth with the smallest number of those (0 is top priority, then 1, then 2).
%H A276657 Max Alekseyev, <a href="/A276657/b276657.txt">Table of n, a(n) for n = 1..100</a>
%F A276657 a(n) = A192009(n) / n.
%F A276657 For n > 1, a(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.
%t A276657 r[n_] := {ToRules[Reduce[m >= 0 && k >= 0 && 2 m + 3 k == n, {m, k}, Integers]]}; f[{m_, k_}] := (m + k - 1)!*Binomial[m + k, m]*2^k*k!*(m + k)!; a[n_] := Total[f /@ ({m, k} /. r[n])]; a[1] = 1; Array[a, 26] (* _Jean-François Alcover_, Sep 13 2016 *)
%o A276657 (PARI) { A276657(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; }
%Y A276657 Cf. A192009 (labeled case).
%Y A276657 Cf. A095236, A192008.
%K A276657 nonn
%O A276657 1,3
%A A276657 _Max Alekseyev_, Sep 11 2016