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A320452
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Number of possible states when placing n tokens of 2 alternating types on 2 piles.
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2
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1, 2, 4, 8, 15, 28, 52, 96, 177, 326, 600, 1104, 2030, 3732, 6858, 12600, 23144, 42504, 78048, 143296, 263068, 482904, 886392, 1626912, 2985943, 5480012, 10056946, 18456056, 33868851, 62151788, 114050884, 209284710, 384034660
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OFFSET
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0,2
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COMMENTS
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Piles start empty and have no height limit. A token can only be placed on top of a pile. The starting token is fixed.
Up to a(11) the terms are matching A008937(n+1).
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LINKS
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EXAMPLE
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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:
B B
A A B B B B B B A A
B B B BB A AB BA A A AB BA A BB B B B
A_ AB AA AA AB AB AB AB BA BA BA BA AA AA BA _A
All states are different, except the 13th state is a duplicate of the 4th.
Hence a(4)=15.
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PROG
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(Python)
def fill(patterns, state_in, ply_nr, n_plies, n_players, n_stacks):
....if ply_nr>=n_plies:
........patterns.add(tuple(state_in))
....else:
........symbol=chr(ord('A')+ply_nr%n_players)
........for st in range(n_stacks):
............state_out=list(state_in)
............state_out[st]+=symbol
............fill(patterns, state_out, ply_nr+1, n_plies, n_players, n_stacks)
....n_plies, n_players, n_stacks = n, 2, 2
....patterns=set()
....state=[""]*n_stacks
....fill(patterns, state, 0, n_plies, n_players, n_stacks)
....return len(patterns)
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CROSSREFS
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For 2 token types on 3 piles, see A320731.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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