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A236532
Triangle T(n,k) read by rows: T(n,k) = floor(n*k/(n+k)), with 1 <= k <= n.
1
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, 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, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 0, 1, 2, 3, 3, 4, 4, 4, 5, 5
OFFSET
1,10
COMMENTS
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
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)
FORMULA
T(n, n) = floor(n/2). See A004526. - Michel Marcus, Feb 25 2020
EXAMPLE
Triangle begins:
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 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 2 3 3 4 4 4 5 5 5 6
0 1 2 3 3 4 4 4 5 5 5 6 6
0 1 2 3 3 4 4 5 5 5 6 6 6 7
0 1 2 3 3 4 4 5 5 6 6 6 6 7 7
0 1 2 3 3 4 4 5 5 6 6 6 7 7 7 8
0 1 2 3 3 4 4 5 5 6 6 7 7 7 7 8 8
0 1 2 3 3 4 5 5 6 6 6 7 7 7 8 8 8 9
PROG
(Python)
for n in range(1, 21):
for k in range(1, n+1):
print n*k // (n+k),
#print
(PARI) T(n, k)={n*k\(n+k)} \\ Andrew Howroyd, Feb 24 2020
CROSSREFS
Sequence in context: A127506 A353433 A007968 * A077763 A030218 A281388
KEYWORD
nonn,easy,tabl
AUTHOR
Alex Ratushnyak, Jan 27 2014
STATUS
approved