A089484 -id:A089484 - cp's OEIS frontend

A346737 Number of configurations of the 5 X 3 variant of the sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners.

1, 2, 4, 9, 21, 42, 89, 164, 349, 644, 1349, 2473, 5109, 9110, 18489, 32321, 64962, 112445, 223153, 378761, 740095, 1231589, 2364342, 3847629, 7246578, 11506172, 21233764, 32854049, 59293970, 89146163, 157015152, 228894783, 392648931, 553489877, 922382155

Offset: 0

Ben Whitmore, Jul 31 2021

This sequence was originally computed by Richard Korf, but the full sequence was not included in his paper. It was later re-computed by Tomas Rokicki.

			Starting from the solved configuration
   1  2  3  4  5
   6  7  8  9 10
  11 12 13 14
the unique configuration requiring 84 moves is
   5  4  3  2  1
  10  9  8  7  6
     14 13 12 11

Ben Whitmore, Table of n, a(n) for n = 0..84
Richard Korf, Linear-time Disk-Based Implicit Graph Search, Journal of the ACM 55 (2008), No. 6.
Tomas Rokicki, Twenty-Four puzzle, some observations, 2011.

Cf. A090033, A090034, A090035, A090036, A090167, A346736, A090166, A089473, A089484.

# alst(), moves(), swap() in A089473
print(alst("-123456789abcde", (5, 3), v=True)) # Michael S. Branicky, Jul 31 2021

A090377 Number of configurations that require a minimum of n moves to be reached, starting with the empty square in one of the corners of an infinitely large extension of Sam Loyd's sliding block 15-puzzle.

Original entry on oeis.org

1, 2, 4, 10, 26, 66, 173, 456, 1230, 3318, 9066, 24768, 68304, 188370, 523083, 1452560, 4054708, 11318926

Offset: 0

Hugo Pfoertner, Nov 27 2003

The first n terms of this sequence coincide with the first n terms of the corresponding sequences for n X n sliding block puzzles (see Cross-references).

Cf. A089473 (3 X 3 puzzle), A089484 (4 X 4), A090031 (5 X 5), A090032 (6 X 6).

# uses alst(), swap() in A089473
nn = 13
start = "".join([chr(i) for i in range(45, 45+(nn+1)**2)]) # chr(45) is "-"
print(alst(start, (nn+1, nn+1), maxd=nn)) # Michael S. Branicky, Jan 02 2021

a(10)-a(17) from Michael S. Branicky, Dec 28 2020

cp's OEIS Frontend

A346737 Number of configurations of the 5 X 3 variant of the sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners.

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