OFFSET
2,3
COMMENTS
If (s,t) is a pair in the sequence, then (s+3u,t-3u) is also a pair in the sequence for any integer u such that both s+3u > 0 and t-3u > 0.
FORMULA
i) If n is even, n=2k, then its pairs are: (k+3p,k-3p), where p is an integer such that both k+3p > 0 and k-3p > 0. ii) If n is odd, n=2k+1, then its pairs are (k+3p+2,k-3p-1), where p is an integer such that both k+3p+2 > 0 and k-3p-1 > 0.
EXAMPLE
The table starts with rows of even length at n=2 as:
(1,1)
(empty)
(2,2)
(4,1),(1,4)
(3,3)
(5,2),(2,5)
MAPLE
A181633_row := proc(n)
local L, a, b;
L := [] ;
for a from n-1 to 1 by -1 do
b := n-a ;
if modp(a, 3) = modp(b, 3) then
L := [op(L), a, b] ;
end if;
end do:
L ;
end proc: # R. J. Mathar, May 14 2016
MATHEMATICA
Table[Select[Transpose@{#, n - #}, Mod[First@ #, 3] == Mod[Last@ #, 3] &] &@ Reverse@ Range[1, n - 1], {n, 18}] // Flatten (* Michael De Vlieger, May 15 2016 *)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Florentin Smarandache (smarand(AT)unm.edu), Nov 03 2010
EXTENSIONS
Edited by R. J. Mathar, May 14 2016
STATUS
approved