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

Author

Ben Whitmore, Nov 01 2015

Keywords

• easy
• nonn

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.

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, 15 Puzzle

Crossrefs

Cf. A087725, A090031, A088020.

Programs

Mathematica

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

Formula

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

Extensions

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