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A089484 Number of configurations of the sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners. 13
1, 2, 4, 10, 24, 54, 107, 212, 446, 946, 1948, 3938, 7808, 15544, 30821, 60842, 119000, 231844, 447342, 859744, 1637383, 3098270, 5802411, 10783780, 19826318, 36142146, 65135623, 116238056, 204900019, 357071928, 613926161, 1042022040 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The last term is a(80). The total number of possible configurations of an m X m sliding block puzzle is (m*m)!/2 = A088020(4)/2, therefore, Sum_i (i=0..80) a(i) = 16!/2 = 10461394944000.
REFERENCES
See A087725.
LINKS
Herman Jamke, Table of n, a(n) for n = 0..80 (complete sequence)
Herbert Kociemba, 15-Puzzle Optimal Solver
R. E. Korf and P. Schultze, Large-Scale Parallel Breadth-First Search
PROG
(Python) # alst(), moves(), swap() in A089473
start, shape = "-123456789ABCDEF", (4, 4)
alst(start, shape, v=True) # Michael S. Branicky, Dec 31 2020
CROSSREFS
Sequence in context: A350881 A018114 A356695 * A132732 A275447 A095214
KEYWORD
fini,full,nonn
AUTHOR
Hugo Pfoertner, Nov 25 2003
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 19 2006
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)