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 A151944 Square array read by antidiagonals: T(m,n) = maximal number of moves required for the m X n generalization of the sliding block 15-puzzle (or fifteen-puzzle). 2
 0, 1, 1, 2, 6, 2, 3, 21, 21, 3, 4, 36, 31, 36, 4, 5, 55, 53, 53, 55, 5, 6, 80, 84, 80, 84, 80, 6, 7, 108 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS See A087725 for more about this problem and its history. LINKS Richard Korf, Linear-time Disk-Based Implicit Graph Search, Journal of the ACM 55 (2008), No. 6. Anton Kulchitsky, Comments on the Fifteen Puzzle [The entries for the 3x4 puzzle are wrong.  The second "8" should be "11" in each of the 18 cases.- Brian Almond, Oct 10 2021] EXAMPLE Array begins: .n\m...1...2...3...4...5...6...7...8...9 .---------------------------------------- .1.|...0...1...2...3...4...5...6...7...8 .2.|...1...6..21..36..55..80.108.140 .3.|...2..21..31..53..84 .4.|...3..36..53..80 .5.|...4..55..84 .6.|...5..80 .7.|...6.108 .8.|...7.140 .9.|...8 PROG # (Python) # alst(), moves(), swap() in A089473 def T(m, n):  # chr(45) is '-'     start, shape = "".join(chr(45+i) for i in range(m*n)), (m, n)     return len(alst(start, shape))-1 def auptodiag(maxd):     for d in range(1, maxd+1):         for m in range(1, d+1):             n = d-m+1             print(T(m, d-m+1), end=", ") auptodiag(5) # Michael S. Branicky, Aug 02 2021 CROSSREFS Main diagonal: A087725. Row 2: A151943. Cf. A090033 same as this sequence, but written as triangle. Sequence in context: A334188 A265993 A115009 * A073094 A194953 A057606 Adjacent sequences:  A151941 A151942 A151943 * A151945 A151946 A151947 KEYWORD nonn,tabl,more AUTHOR Anton Kulchitsky (kulchits(AT)arsc.edu), Aug 14 2009, Aug 16 2009 EXTENSIONS Extensions from Korf's 2008 publication, with corrections, Tomas Rokicki, Aug 17 2011 STATUS approved

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Last modified August 13 18:00 EDT 2022. Contains 356107 sequences. (Running on oeis4.)