OFFSET
1,2
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) = -max(i,j)*((-1)^i-1)/2+min(i,j)*((-1)^i+1)/2, if i>=j
a(n) = max(i,j)*((-1)^j+1)/2-min(i,j)*((-1)^j-1)/2, if i<j,
where t = floor((-1+sqrt(8*n-7))/2), i = n-t*(t+1)/2, j = (t*t+3*t+4)/2-n.
EXAMPLE
The start of the sequence as triangle array read by rows:
1;
2,1;
1,2,3;
4,2,3,1;
1,4,3,2,5;
6,2,4,3,5,1;
1,6,3,4,5,2,7;
...
Row number k contains permutation numbers form 1 to k.
PROG
(Python)
t=int((math.sqrt(8*n-7) - 1)/ 2)
i=n-t*(t+1)//2
j=(t*t+3*t+4)//2-n
if i>=j:
result=-max(i, j)*((-1)**i-1)/2+min(i, j)*((-1)**i+1)/2
else:
result= max(i, j)*((-1)**j+1)/2-min(i, j)*((-1)**j-1)/2
CROSSREFS
KEYWORD
nonn
AUTHOR
Boris Putievskiy, Jan 10 2013
STATUS
approved