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%I #30 Sep 08 2022 08:44:37
%S 1,12,66,220,495,792,924,792,495,220,66,12,1
%N Binomial coefficient C(12,n).
%C Row 12 of A007318.
%C Also number of positions that are exactly n moves from the starting position in the Orbix Type 1 puzzle. This is the number of positions that can be reached in n moves from the start, but which cannot be reached in fewer than n moves. A puzzle in the Rubik cube family. The total number of distinct positions is 4096. Here positions differing by rotations or reflections are considered distinct.
%C If the sequence is extended by trailing zeros, its binomial transform yields A010965. - _R. J. Mathar_, Sep 19 2008
%H Jaap Scherphuis, <a href="http://www.jaapsch.net/puzzles/">Puzzle Pages</a>
%p seq(binomial(12,n), n=0..12); # _Nathaniel Johnston_, Jun 23 2011
%t q = 12; Join[{a = 1}, Table[a = (q - n)*a/(n + 1), {n, 0, q - 1}]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 09 2011 *)
%t Binomial[12,Range[0,12]] (* _Harvey P. Dale_, Jul 02 2018 *)
%o (Sage) [binomial(12,m) for m in range(13)] # _Zerinvary Lajos_, Apr 21 2009
%o (Magma) [Binomial(12, n): n in [0..12]]; // _Vincenzo Librandi_, Jun 12 2013
%Y Cf. A010926-A011001, A080560-A080564.
%K nonn,fini,full,easy
%O 0,2
%A _N. J. A. Sloane_
%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 15 2007
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