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A181633 Irregular triangle read by rows, where row n contains the pairs [q,q'] of all compositions n=q+q' with q,q'>0 and q == q' (mod 3). 1
1, 1, 2, 2, 4, 1, 1, 4, 3, 3, 5, 2, 2, 5, 7, 1, 4, 4, 1, 7, 6, 3, 3, 6, 8, 2, 5, 5, 2, 8, 10, 1, 7, 4, 4, 7, 1, 10, 9, 3, 6, 6, 3, 9, 11, 2, 8, 5, 5, 8, 2, 11, 13, 1, 10, 4, 7, 7, 4, 10, 1, 13, 12, 3, 9, 6, 6, 9, 3, 12, 14, 2, 11, 5, 8, 8, 5, 11, 2, 14, 16, 1, 13, 4, 10, 7, 7, 10, 4, 13, 1, 16, 15, 3, 12, 6, 9, 9, 6, 12, 3, 15 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Cf. A181634 (where q and q' may be zero), A008611 (half of the row lengths).
Sequence in context: A214741 A243487 A143485 * A245204 A099320 A206714
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

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Last modified April 18 13:10 EDT 2024. Contains 371780 sequences. (Running on oeis4.)