A264040 Number of possible permutations of the n X n generalization of the sliding block 15-puzzle.

1, 12, 181440, 10461394944000, 7755605021665492992000000, 185996663394950608733999724075417600000000, 304140932017133780436126081660647688443776415689605120000000000, 63443466092942082051716694667580740401432758087272596099400947187607352115200000000000000

Offset

1,2

Comments

For n > 1, of the permutations that can be reached by disassembling the puzzle and replacing the tiles, exactly half of them can be reached by sliding the tiles.

Links

Table of n, a(n) for n=1..8.

Eric Weisstein's World of Mathematics, 15 Puzzle

Formula

a(1) = 1; a(n) = (n^2)!/2 for n > 1.

Example

a(4) = 10461394944000 because the standard 4 X 4 version of the 15-puzzle has exactly 10461394944000 permutations that can be reached by sliding the tiles.

Mathematica

a[n_] := If[n == 1, 1, (n^2)!/2]

Crossrefs

Cf. A087725, A090031, A088020.

Sequence in context: A055323 A368686 A333099 * A013796 A055312 A365242

Adjacent sequences: A264037 A264038 A264039 * A264041 A264042 A264043

Keyword

easy,nonn

Author

Ben Whitmore, Nov 01 2015

Extensions

a(1) added by Franklin T. Adams-Watters, Nov 11 2015

Status

approved