%I A096259
%S A096259 1,2,6,24,70,180,294,112,270,900,330,792
%N A096259 Longest period of an abstract version of the game of Go on a 1 X n board.
%C A096259 Rules: 1. If a set of a player's stones has no "open edge" then the other 
               player get the set of stones.
%C A096259 2. If the sets of both player's stones has no "open edge" in a configuration, 
               then a player who made this configuration get the set of the other 
               player's stone.
%C A096259 3. A player never make a configuration in which his stones have no open 
               edge and the other player's stones have an open edge.
%C A096259 A board is represented as follows.
%C A096259 + + + +
%C A096259 + o x +
%C A096259 + + + +
%C A096259 "o" means a white stone, "x" means a black stone.
%C A096259 "Open edge" : An edge which has one node without a stone. Example:
%C A096259 + x x +
%C A096259 x o o x
%C A096259 + x x +
%C A096259 The center set of white stones has no "open edge", so black player gets 
               them. Six black stones have "open edges" like this : "x +".
%C A096259 Note that the rules do not specify when a player wins, so the game never 
               terminates.
%F A096259 For 4<=n, a(n) = n * 2^p * ( Sum_{0<=k<=m} ( Sum_{0<=i<=h_k} n_k/2^i 
               ) - 1 ) where p = m Mod 2, n_0 = n, n_k = n - [n_{k-1}/2^(h_{k-1}+1)] 
               - 1, 2^h_k is the highest power of two dividing n_k: n_m/2^h_m = 
               1.
%e A096259 The case n=3:
%e A096259 t 1 2 3 3 4 4 5 6 6 7 7
%e A096259 + x x x x x + x x + x x
%e A096259 + + + x x x + + o o o +
%e A096259 + + o o + o o o o o o +
%e A096259 t=1 and t=7 are the same, so the period is 6.
%e A096259 a(12) = 12*2^0*(12 +6 +3 +10 +5 +9 +7 +8 +4 +2 +1 -1) =792
%Y A096259 Cf. A007565, A048289, A137604-A137607.
%Y A096259 Sequence in context: A022917 A107762 A027562 this_sequence A087645 A107761 
               A147943
%Y A096259 Adjacent sequences: A096256 A096257 A096258 this_sequence A096260 A096261 
               A096262
%K A096259 nonn
%O A096259 1,2
%A A096259 Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), Aug 01 2004; revised 
               Apr 23 2008