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Number of configurations that require a minimum of n moves to be reached, starting with the empty square at mid-side of a boundary of an infinitely large extension of Sam Loyd's sliding block 15-puzzle.
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%I #12 Jan 02 2021 14:57:34

%S 1,3,7,19,53,147,409,1151,3255,9241,26267,74895,213775,611463,1750277,

%T 5017901

%N Number of configurations that require a minimum of n moves to be reached, starting with the empty square at mid-side of a boundary of an infinitely large extension of Sam Loyd's sliding block 15-puzzle.

%C Next term (unconfirmed): a(6)=409. If started with the empty square at mid-side of a boundary, the number of configurations reachable in the first floor((n-1)/2) moves in an n X n sliding block puzzle are given by this sequence.

%o (Python) # uses alst(), swap() in A089473

%o nn = 24

%o mid = (nn-1)//2

%o startlst = [chr(i) for i in range(45, 45+nn**2)] # chr(45) is "-"

%o startlst[0], startlst[mid] = startlst[mid], startlst[0]

%o start = "".join(startlst)

%o print(alst(start, (nn, nn), maxd=mid)) # _Michael S. Branicky_, Jan 02 2021

%Y Cf. A089483 (3 X 3 puzzle started with empty square at mid-side), A090165.

%K more,nonn

%O 0,2

%A _Hugo Pfoertner_, Nov 27 2003

%E a(6) confirmed and a(7)-a(15) from _Michael S. Branicky_, Dec 28 2020