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.
Up to a(11) the terms are matching A008937(n+1).
LINKS
Martin Fuller, Table of n, a(n) for n = 0..40
Alistair Hartley Folster, Counting reachable positions in a simplified model of connect four, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 131. 57-65 (2026).
EXAMPLE
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.
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 A320452(n):
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)
CROSSREFS
KEYWORD
nonn
AUTHOR
Bert Dobbelaere, Oct 20 2018
EXTENSIONS
a(33) onwards from Martin Fuller, Apr 09 2025
STATUS
approved