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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

Table of n, a(n) for n=0..23.

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.)