A194885 Write n = C(i,4)+C(j,3)+C(k,2)+C(l,1) with i>j>k>l>=0; let L[n] = [i,j,k,l]; sequence gives list of quadruples L[n], n >= 0.

3, 2, 1, 0, 4, 2, 1, 0, 4, 3, 1, 0, 4, 3, 2, 0, 4, 3, 2, 1, 5, 2, 1, 0, 5, 3, 1, 0, 5, 3, 2, 0, 5, 3, 2, 1, 5, 4, 1, 0, 5, 4, 2, 0, 5, 4, 2, 1, 5, 4, 3, 0, 5, 4, 3, 1, 5, 4, 3, 2, 6, 2, 1, 0, 6, 3, 1, 0, 6, 3, 2, 0, 6, 3, 2, 1, 6, 4, 1, 0, 6, 4, 2, 0, 6, 4, 2, 1, 6, 4, 3, 0, 6, 4, 3, 1, 6, 4, 3, 2, 6, 5, 1, 0, 6, 5, 2, 0, 6, 5, 2, 1, 6, 5, 3, 0, 6, 5, 3, 1, 6

Offset: 0

Author

N. J. A. Sloane, Sep 04 2011

Keywords

• nonn
• tabf

Comments

Each n >= 0 has a unique representation as n = C(i,4)+C(j,3)+C(k,2)+C(l.1) with i>j>k>l>=0. This is the combinatorial number system of degree t = 4, where we get [A194882, A194883, A194884, A127324]. For degree t = 3 see A194847.

Examples

			List of quadruples begins:
[3, 2, 1, 0]
[4, 2, 1, 0]
[4, 3, 1, 0]
[4, 3, 2, 0]
[4, 3, 2, 1]
[5, 2, 1, 0]
[5, 3, 1, 0]
[5, 3, 2, 0]
[5, 3, 2, 1]
[5, 4, 1, 0]
[5, 4, 2, 0]
...
		

References

• D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3, Eq. (20), p. 360.

Crossrefs

The four columns are [A194882, A194883, A194885, A127324], or equivalently [A127321+3, A127322+2, A127323+1, A127324].