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A194885
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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.
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4
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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
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OFFSET
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0,1
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COMMENTS
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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.
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3, Eq. (20), p. 360.
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LINKS
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EXAMPLE
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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]
...
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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