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A056558
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Third tetrahedral coordinate, i.e., tetrahedron with T(t,n,k)=k; succession of growing finite triangles with increasing values towards bottom right.
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29
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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, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5
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OFFSET
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0,10
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COMMENTS
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Alternatively, write n = C(i,3)+C(j,2)+C(k,1) with i>j>k>=0; sequence gives k values. See A194847 for further information about this interpretation.
If {(X,Y,Z)} are triples of nonnegative integers with X>=Y>=Z ordered by X, Y and Z, then X=A056556(n), Y=A056557(n) and Z=A056558(n)
This is a 'Matryoshka doll' sequence with alpha=0 (cf. A000292 and A000178). - Peter Luschny, Jul 14 2009
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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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FORMULA
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EXAMPLE
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First triangle: [0]; second triangle: [0; 0 1]; third triangle: [0; 0 1; 0 1 2]; ...
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MAPLE
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seq(seq(seq(i, i=0..k), k=0..n), n=0..6); # Peter Luschny, Sep 22 2011
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MATHEMATICA
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Table[i, {k, 0, 7}, {j, 0, k}, {i, 0, j}] // Flatten (* Robert G. Wilson v, Sep 27 2011 *)
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PROG
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(Haskell)
import Data.List (inits)
a056558 n = a056558_list !! n
a056558_list = concatMap (concat . init . inits . enumFromTo 0) [0..]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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