A220415 Table T(n,k)= floor(n/k)+ floor(k/n), n,k >0 read by antidiagonals.

2, 2, 2, 3, 2, 3, 4, 1, 1, 4, 5, 2, 2, 2, 5, 6, 2, 1, 1, 2, 6, 7, 3, 1, 2, 1, 3, 7, 8, 3, 2, 1, 1, 2, 3, 8, 9, 4, 2, 1, 2, 1, 2, 4, 9, 10, 4, 2, 1, 1, 1, 1, 2, 4, 10, 11, 5, 3, 2, 1, 2, 1, 2, 3, 5, 11

Offset: 1

Author

Boris Putievskiy, Dec 21 2012

Keywords

• nonn
• tabl

Examples

			The start of the sequence as triangle array read by rows:
  2;
  2,2;
  3,2,3;
  4,1,1,4;
  5,2,2,2,5;
  6,2,1,1,2,6;
  ...
		

Links

• Boris Putievskiy, Rows n = 1..140 of triangle, flattened
• Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Crossrefs

Cf. A002260, A004736.

Programs

Python

t=int((math.sqrt(8*n-7) - 1)/ 2)
a = n-t*(t+1)/2
b= (t*t+3*t+4)/2-n
m= int(a/b)+int(b/a)

Formula

a(n) = floor(A002260(n)/A004736(n))+floor(A004736(n)/A002260(n)) or

a(n) = floor((n-t*(t+1)/2)/((t*t+3*t+4)/2-n)) + floor(((t*t+3*t+4)/2-n)/(n-t*(t+1)/2)), where t=floor((-1+sqrt(8*n-7))/2).