OFFSET
0,15
COMMENTS
Alternatively, write n = C(i,4)+C(j,3)+C(k,2)+C(l,1) with i>j>k>l>=0; sequence gives k values. 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].
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 analogs of the three-dimensional A056556, A056557 and A056558.
This is a 'Matryoshka doll' sequence with alpha=0 (cf. A055462 and A000332), seq(seq(seq(seq(i,i=alpha..k),k=alpha..n),n=alpha..m),m=alpha..4). - Peter Luschny, Jul 14 2009
REFERENCES
D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3, Eq. (20), p. 360.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
FORMULA
EXAMPLE
MAPLE
seq(seq(seq(seq(i, i=0..k), k=0..n), n=0..m), m=0..5); # Peter Luschny, Sep 22 2011
MATHEMATICA
Table[i, {m, 0, 5}, {k, 0, m}, {j, 0, k}, {i, 0, j}] // Flatten (* Robert G. Wilson v, Sep 27 2011 *)
PROG
(Haskell)
import Data.List (inits)
a127324 n = a127324_list !! n
a127324_list = concatMap (concatMap concat .
inits . inits . enumFromTo 0) $ enumFrom 0
-- Reinhard Zumkeller, Jun 01 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Graeme McRae, Jan 10 2007
STATUS
approved