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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

Table of n, a(n) for n=2..103.

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

Adjacent sequences:  A181630 A181631 A181632 * A181634 A181635 A181636

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 March 26 04:55 EDT 2017. Contains 284111 sequences.