A090378 - OEIS

A090378

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.

1, 3, 7, 19, 53, 147, 409, 1151, 3255, 9241, 26267, 74895, 213775, 611463, 1750277, 5017901

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OFFSET

0,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..15.

PROG

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

nn = 24

mid = (nn-1)//2

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

startlst[0], startlst[mid] = startlst[mid], startlst[0]

start = "".join(startlst)

print(alst(start, (nn, nn), maxd=mid)) # Michael S. Branicky, Jan 02 2021

CROSSREFS

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