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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

Table of n, a(n) for n=1..30.

Richard Korf, Linear-time Disk-Based Implicit Graph Search, Journal of the ACM 55 (2008), No. 6.

Anton Kulchitsky, Comments on the Fifteen Puzzle

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 October 21 19:16 EDT 2021. Contains 348155 sequences. (Running on oeis4.)