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%I #19 Nov 06 2018 13:26:42
%S 1,2,4,8,15,28,52,96,177,326,600,1104,2030,3732,6858,12600,23144,
%T 42504,78048,143296,263068,482904,886392,1626912,2985943,5480012,
%U 10056946,18456056,33868851,62151788,114050884,209284710,384034660
%N Number of possible states when placing n tokens of 2 alternating types on 2 piles.
%C Piles start empty and have no height limit. A token can only be placed on top of a pile. The starting token is fixed.
%C Up to a(11) the terms are matching A008937(n+1).
%e With alternating symbols A and B on two piles (starting with A), the following states emerge after placing 4 symbols in all 2^4 possible ways:
%e B B
%e A A B B B B B B A A
%e B B B BB A AB BA A A AB BA A BB B B B
%e A_ AB AA AA AB AB AB AB BA BA BA BA AA AA BA _A
%e All states are different, except the 13th state is a duplicate of the 4th.
%e Hence a(4)=15.
%o (Python)
%o def fill(patterns, state_in, ply_nr, n_plies, n_players, n_stacks):
%o ....if ply_nr>=n_plies:
%o ........patterns.add(tuple(state_in))
%o ....else:
%o ........symbol=chr(ord('A')+ply_nr%n_players)
%o ........for st in range(n_stacks):
%o ............state_out=list(state_in)
%o ............state_out[st]+=symbol
%o ............fill(patterns, state_out, ply_nr+1, n_plies, n_players, n_stacks)
%o def A320452(n):
%o ....n_plies,n_players,n_stacks = n,2,2
%o ....patterns=set()
%o ....state=[""]*n_stacks
%o ....fill(patterns, state, 0, n_plies, n_players, n_stacks)
%o ....return len(patterns)
%Y For 2 token types on 3 piles, see A320731.
%K nonn,more
%O 0,2
%A _Bert Dobbelaere_, Oct 20 2018
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