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

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.

Sequence in context: A115254 A222324 A007180 * A059506 A007575 A026299

Adjacent sequences: A090375 A090376 A090377 * A090379 A090380 A090381

Keyword

more,nonn

Author

Hugo Pfoertner, Nov 27 2003

Extensions

a(6) confirmed and a(7)-a(15) from Michael S. Branicky, Dec 28 2020

Status

approved