A127322 Second 4-dimensional hyper-tetrahedral coordinate; 4-D analog of A056557.

0, 0, 1, 1, 1, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 0

Author

Graeme McRae, Jan 10 2007

Keywords

• nonn

Comments

If {(W,X,Y,Z)} are 4-tuples of nonnegative integers with W>=X>=Y>=Z ordered by W, X, Y and Z, then W=A127321(n), X=A127322(n), Y=A127323(n) and Z=A127324(n). These sequences are the four-dimensional analog of the three-dimensional A056556, A056557 and A056558.

Examples

			a(23)=2 because a(A000332(2+3)+A000292(2)) = a(A000332(2+3)+A000292(3)-1) = 2, so a(19) = a(24) = 2.
See A127321 for a table of A127321, A127322, A127323, A127324.
		

Crossrefs

Cf. A127321, A127323, A127324, A056556, A056557, A056558, A000332, A000292, A000217.

Formula

For W>=X>=0, a(A000332(W+3)+A000292(X)) = a(A000332(W+3)+A000292(X+1)-1) = X A127322(n+1) = A127321(n)==A127324(n) ? 0 : A127322(n)==A127324(n) ? A127322(n)+1 : A127322(n)