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 A127324 Fourth 4-dimensional hyper-tetrahedral coordinate; 4-D analog of A056558. 14
 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4 (list; graph; refs; listen; history; text; internal format)
 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 For W>=X>=Y>=Z>=0, a(A000332(W+3)+A000292(X)+A000217(Y)+Z) = Z A127322(n+1) = A127321(n)==A127324(n) ? 0 : A127322(n)==A127324(n) ? 0 : A127323(n)==A127324(n) ? 0 : A127324(n)+1 EXAMPLE See A127321 for a table of A127321, A127322, A127323, A127324 See A127327 for a table of A127324, A127325, A127326, A127327 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 Cf. A127321, A127322, A127323, A056556, A056557, A056558, A000332, A000292, A000217. Cf. A002262, A056558. Sequence in context: A316717 A085981 A243224 * A083917 A117974 A193426 Adjacent sequences:  A127321 A127322 A127323 * A127325 A127326 A127327 KEYWORD nonn AUTHOR Graeme McRae, Jan 10 2007 STATUS approved

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Last modified November 19 14:52 EST 2018. Contains 317352 sequences. (Running on oeis4.)