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 A127321 First 4-dimensional hyper-tetrahedral coordinate; repeat m C(m+3,4) times; 4-D analog of A056556. 8

%I

%S 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,

%T 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,

%U 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

%N First 4-dimensional hyper-tetrahedral coordinate; repeat m C(m+3,4) times; 4-D analog of A056556.

%C 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.

%F For W>=0, a(A000332(W+3)) = a(A000332(W+4)-1) = W A127321(n+1) = A127321(n)==A127324(n) ? A127321(n)+1 : A127321(n)

%e a(23)=3 because a(A000332(3+3)) = a(A000332(3+4)-1) = 3, so a(15) = a(34) = 3.

%e Table of A127321, A127322, A127323, A127324:

%e n W,X,Y,Z

%e 0 0,0,0,0

%e 1 1,0,0,0

%e 2 1,1,0,0

%e 3 1,1,1,0

%e 4 1,1,1,1

%e 5 2,0,0,0

%e 6 2,1,0,0

%e 7 2,1,1,0

%e 8 2,1,1,1

%e 9 2,2,0,0

%e 10 2,2,1,0

%e 11 2,2,1,1

%e 12 2,2,2,0

%e 13 2,2,2,1

%e 14 2,2,2,2

%e 15 3,0,0,0

%e 16 3,1,0,0

%e 17 3,1,1,0

%e 18 3,1,1,1

%e 19 3,2,0,0

%e 20 3,2,1,0

%e 21 3,2,1,1

%e 22 3,2,2,0

%e 23 3,2,2,1

%Y Cf. A127322, A127323, A127324, A056556, A056557, A056558, A000332, A000292, A000217.

%K nonn

%O 0,6

%A _Graeme McRae_, Jan 10 2007

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Last modified February 22 16:40 EST 2019. Contains 320399 sequences. (Running on oeis4.)