cp's OEIS Frontend

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.

%I A090378 #12 Jan 02 2021 14:57:34
%S A090378 1,3,7,19,53,147,409,1151,3255,9241,26267,74895,213775,611463,1750277,
%T A090378 5017901
%N 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.
%C A090378 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 A090378 (Python) # uses alst(), swap() in A089473
%o A090378 nn = 24
%o A090378 mid = (nn-1)//2
%o A090378 startlst = [chr(i) for i in range(45, 45+nn**2)] # chr(45) is "-"
%o A090378 startlst[0], startlst[mid] = startlst[mid], startlst[0]
%o A090378 start = "".join(startlst)
%o A090378 print(alst(start, (nn, nn), maxd=mid)) # _Michael S. Branicky_, Jan 02 2021
%Y A090378 Cf. A089483 (3 X 3 puzzle started with empty square at mid-side), A090165.
%K A090378 more,nonn
%O A090378 0,2
%A A090378 _Hugo Pfoertner_, Nov 27 2003
%E A090378 a(6) confirmed and a(7)-a(15) from _Michael S. Branicky_, Dec 28 2020