A220415 - OEIS

%I #19 Feb 16 2022 18:24:45

%S 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,

%T 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

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

%H Boris Putievskiy, <a href="/A220415/b220415.txt">Rows n = 1..140 of triangle, flattened</a>

%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.

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

%F 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).

%e The start of the sequence as triangle array read by rows:

%e   2;

%e   2,2;

%e   3,2,3;

%e   4,1,1,4;

%e   5,2,2,2,5;

%e   6,2,1,1,2,6;

%e   ...

%o (Python)

%o t=int((math.sqrt(8*n-7) - 1)/ 2)

%o a = n-t*(t+1)/2

%o b= (t*t+3*t+4)/2-n

%o m= int(a/b)+int(b/a)

%Y Cf. A002260, A004736.

%K nonn,tabl

%O 1,1

%A _Boris Putievskiy_, Dec 21 2012