A010928 Binomial coefficient C(12,n).

1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full
• easy

Comments

Row 12 of A007318.

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.

If the sequence is extended by trailing zeros, its binomial transform yields A010965. - R. J. Mathar, Sep 19 2008

Links

• Jaap Scherphuis, Puzzle Pages

Crossrefs

Cf. A010926-A011001, A080560-A080564.

Programs

Magma

[Binomial(12, n): n in [0..12]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(12,n), n=0..12); # Nathaniel Johnston, Jun 23 2011

Mathematica

q = 12; Join[{a = 1}, Table[a = (q - n)*a/(n + 1), {n, 0, q - 1}]] (* Vladimir Joseph Stephan Orlovsky, Jul 09 2011 *)
Binomial[12,Range[0,12]] (* Harvey P. Dale, Jul 02 2018 *)

Sage

[binomial(12,m) for m in range(13)] # Zerinvary Lajos, Apr 21 2009

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 15 2007