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%I #28 Jan 10 2019 23:06:41
%S 0,1,1,2,1,2,2,3,2,3,2,3,4,3,4,3,4,5,2,3,4,3,4,5,4,5,6,3,4,5,3,4,5,6,
%T 4,5,6,4,5,6,7,5,6,7,5,6,7,8,3,4,5,6,4,5,6,7,5,6,7,8,6,7,8,9,4,5,6,7,
%U 4,5,6,7,8,5,6,7,8,5,6,7,8,9,6,7,8,9,6,7,8,9,10
%N Three-dimensional array read by shells: S(i, j, k) = i + j + k; i >= 0, j >= 0, k >= 0.
%C The triples (i,j,k) are ordered first by maximal coordinate, and then lexicographically. - _Charlie Neder_, Dec 23 2018
%H Charlie Neder, <a href="/A260617/b260617.txt">Table of n, a(n) for n = 1..1000</a>
%H Matthew Campbell, <a href="/A260617/a260617.txt">Coordinate Pattern</a>
%e S(0, 0, 0) = 0 + 0 + 0 = 0.
%e S(0, 0, 1) = 0 + 0 + 1 = 1.
%e S(0, 1, 0) = 0 + 1 + 0 = 1.
%e S(0, 1, 1) = 0 + 1 + 1 = 2.
%e S(1, 0, 0) = 1 + 0 + 0 = 1.
%e S(1, 0, 1) = 1 + 0 + 1 = 2.
%e S(1, 1, 0) = 1 + 1 + 0 = 2.
%e S(1, 1, 1) = 1 + 1 + 1 = 3.
%e S(0, 0, 2) = 0 + 0 + 2 = 2.
%e ...
%o (Python)
%o s = lambda x,y,z : x+y+z # function for 3d array
%o i = 1
%o for n in range(0,10):
%o ..for x in range(0,n+1):
%o ....for y in range(0,n+1):
%o ......if (x!=n and y!=n):
%o ........print(i, s(x,y,n))
%o ........i += 1
%o ......else:
%o ........for z in range(0,n+1):
%o ..........print(i, s(x,y,z))
%o ..........i += 1
%o # _Charlie Neder_, Dec 26 2018
%K nonn
%O 1,4
%A _Matthew Campbell_, Sep 17 2015
%E Definition clarified by _Charlie Neder_, Dec 25 2018
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