Inspired by Jaap Scherphuis's excellent web site on generalizations of Rubik's cube, i've added several sequences to the OEIS giving the number of positions that are n moves away from the start in these puzzles. For example: %I A079761 %S A079761 1,9,54,321,1847,9992,50136,227536,870072,1887748,623800,2644 %N A079761 Number of positions that are n moves from the starting position in the 2 X 2 X 2 Rubik cube puzzle. %C A079761 A puzzle in the Rubik cube family. The total number of distinct positions is 3674160. A half-turn is considered to be one move. %D A079761 D. R. Hofstadter, Metamagical Themas, Basic Books, NY, 1985, p. 359. %H A079761 Jaap Scherphuis, <a href="http://www.geocities.com/jaapsch/puzzles/">Puzzle Pages</a> %K A079761 nonn,fini,full,new %O A079761 0,2 %A A079761 njas, Feb 20 2003 Does anyone know the analogous sequence for the 3 X 3 X 3 cube, or even the beginning of that sequence? NJAS