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%I #19 Feb 25 2020 11:49:16
%S 0,0,1,0,1,1,0,1,1,2,0,1,1,2,2,0,1,2,2,2,3,0,1,2,2,2,3,3,0,1,2,2,3,3,
%T 3,4,0,1,2,2,3,3,3,4,4,0,1,2,2,3,3,4,4,4,5,0,1,2,2,3,3,4,4,4,5,5,0,1,
%U 2,3,3,4,4,4,5,5,5,6,0,1,2,3,3,4,4,4,5,5
%N Triangle T(n,k) read by rows: T(n,k) = floor(n*k/(n+k)), with 1 <= k <= n.
%C It appears that the least m such that T(m, n) = n-1 is given by A103505(n) for n>= 1. - _Michel Marcus_, Feb 25 2020
%H Andrew Howroyd, <a href="/A236532/b236532.txt">Table of n, a(n) for n = 1..1275</a> (first 50 rows)
%F T(n, n) = floor(n/2). See A004526. - _Michel Marcus_, Feb 25 2020
%e Triangle begins:
%e 0
%e 0 1
%e 0 1 1
%e 0 1 1 2
%e 0 1 1 2 2
%e 0 1 2 2 2 3
%e 0 1 2 2 2 3 3
%e 0 1 2 2 3 3 3 4
%e 0 1 2 2 3 3 3 4 4
%e 0 1 2 2 3 3 4 4 4 5
%e 0 1 2 2 3 3 4 4 4 5 5
%e 0 1 2 3 3 4 4 4 5 5 5 6
%e 0 1 2 3 3 4 4 4 5 5 5 6 6
%e 0 1 2 3 3 4 4 5 5 5 6 6 6 7
%e 0 1 2 3 3 4 4 5 5 6 6 6 6 7 7
%e 0 1 2 3 3 4 4 5 5 6 6 6 7 7 7 8
%e 0 1 2 3 3 4 4 5 5 6 6 7 7 7 7 8 8
%e 0 1 2 3 3 4 5 5 6 6 6 7 7 7 8 8 8 9
%o (Python)
%o for n in range(1, 21):
%o for k in range(1, n+1):
%o print n*k // (n+k),
%o #print
%o (PARI) T(n,k)={n*k\(n+k)} \\ _Andrew Howroyd_, Feb 24 2020
%Y Cf. A004526, A103505.
%K nonn,easy,tabl
%O 1,10
%A _Alex Ratushnyak_, Jan 27 2014
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