OFFSET
1,2
COMMENTS
Column number k of the table T(n,k) is formula for Cantor antidiagonal order in power k.
LINKS
Boris Putievskiy, Table of n, Rows n = 1 to 30 of triangle, flattened
Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.
FORMULA
As a linear array, the sequence is a(n) = n^A004736(n) or a(n) = n^((t*t+3*t+4)/2 - n), where t=floor((-1+sqrt(8*n-7))/2).
EXAMPLE
Square array T(n,k) begins:
1, 4, 64, 2401, 161051, ...
3, 25, 512, 20736, 1419857, ...
6, 81, 2197, 104976, 7962624, ...
10, 196, 6859, 390625, 33554432, ...
15, 400, 17576, 1185921, 115856201, ...
21, 729, 39304, 3111696, 345025251, ...
...
The start of the sequence as triangle array is:
1;
4, 3;
64, 25, 6;
2401, 512, 91, 10;
161051, 20736, 2197, 196, 15;
...
PROG
(Python)
t=int((math.sqrt(8*n-7) - 1)/ 2)
m=n**((t*t+3*t+4)/2-n)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Boris Putievskiy, Dec 16 2012
STATUS
approved