A236532 Triangle T(n,k) read by rows: T(n,k) = floor(n*k/(n+k)), with 1 <= k <= n.

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

Author

Alex Ratushnyak, Jan 27 2014

Keywords

• nonn
• easy
• tabl

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

Examples

			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
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Crossrefs

Cf. A004526, A103505.

Programs

PARI

T(n,k)={n*k\(n+k)} \\ Andrew Howroyd, Feb 24 2020

Python

for n in range(1, 21):
  for k in range(1, n+1):
    print(n*k // (n+k), end=', ')
  #print() # Uncomment to display as a triangle

Formula

T(n, n) = floor(n/2). See A004526. - Michel Marcus, Feb 25 2020