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 A320731 Number of possible states when placing n tokens of 2 alternating types on 3 piles. 2
 1, 3, 9, 24, 60, 141, 328, 738, 1647, 3618, 7893, 17055, 36619, 78144, 165888, 350619, 738012, 1548279, 3237611, 6752439, 14046525, 29157612, 60396996, 124885167 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Piles start empty and have no height limit. A token can only be placed on top of a pile. The starting token is fixed. LINKS EXAMPLE With alternating symbols A and B on three piles (starting with A), the following states emerge after placing 3 symbols in all 3^3 possible ways:    1    2    3    4    5    6    7    8    9    10   11   12   13   14   15   A                                                                 A   B    B    B    A     A        A           A  A     A         B    B    B   A__  AA_  A_A  AB_  AB_  ABA  A_B  AAB  A_B  BA_  BA_  BAA  AA_  _A_  _AA    16   17   18   19   20   21   22   23   24   25   26   27                                                            A         A     A  A           A        A     A    B    B    B   AAB  _AB  _AB  B_A  BAA  B_A  ABA  _BA  _BA  A_A  _AA  __A 3 pairs of states (numbered (6,22), (8,16) and (12,20)) are identical, all others are different, hence a(3)=24. PROG (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) def A320731(n): ....n_plies, n_players, n_stacks = n, 2, 3 ....patterns=set() ....state=[""]*n_stacks ....fill(patterns, state, 0, n_plies, n_players, n_stacks) ....return len(patterns) CROSSREFS For 2 token types on 2 piles, see A320452. Sequence in context: A086796 A034330 A264685 * A084858 A228820 A335470 Adjacent sequences:  A320728 A320729 A320730 * A320732 A320733 A320734 KEYWORD nonn,more AUTHOR Bert Dobbelaere, Oct 20 2018 STATUS approved

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Last modified September 24 03:26 EDT 2021. Contains 347623 sequences. (Running on oeis4.)