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

1,1

Links

Boris Putievskiy, Rows n = 1..140 of triangle, flattened

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

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).

Example

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;
  ...

Prog

(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)

Crossrefs

Cf. A002260, A004736.

Sequence in context: A194344 A128435 A369219 * A330861 A286565 A219354

Adjacent sequences: A220412 A220413 A220414 * A220416 A220417 A220418

Keyword

nonn,tabl

Author

Boris Putievskiy, Dec 21 2012

Status

approved