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A127321
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First 4-dimensional hyper-tetrahedral coordinate; repeat m C(m+3,3) times; 4-D analog of A056556.
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8
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0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
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OFFSET
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0,6
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = floor(sqrt(5/4 + sqrt(24*n+1)) - 3/2). - Ridouane Oudra, Oct 21 2021
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EXAMPLE
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a(23)=3 because a(A000332(3+3)) = a(A000332(3+4)-1) = 3, so a(15) = a(34) = 3.
n W,X,Y,Z
0 0,0,0,0
1 1,0,0,0
2 1,1,0,0
3 1,1,1,0
4 1,1,1,1
5 2,0,0,0
6 2,1,0,0
7 2,1,1,0
8 2,1,1,1
9 2,2,0,0
10 2,2,1,0
11 2,2,1,1
12 2,2,2,0
13 2,2,2,1
14 2,2,2,2
15 3,0,0,0
16 3,1,0,0
17 3,1,1,0
18 3,1,1,1
19 3,2,0,0
20 3,2,1,0
21 3,2,1,1
22 3,2,2,0
23 3,2,2,1
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MATHEMATICA
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Array[Floor[Sqrt[5/4 + Sqrt[24*# + 1]] - 3/2] &, 105, 0] (* or *)
Flatten@ Array[ConstantArray[#, Binomial[# + 3, 3]] &, 6, 0] (* Michael De Vlieger, Oct 21 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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