A181634 Irregular triangle T(n,k) where row n contains all pairs [a,b] of the compositions n=a+b into nonnegative pairs where a == b (mod 3).

1, 1, 3, 0, 0, 3, 2, 2, 4, 1, 1, 4, 6, 0, 3, 3, 0, 6, 5, 2, 2, 5, 7, 1, 4, 4, 1, 7, 9, 0, 6, 3, 3, 6, 0, 9, 8, 2, 5, 5, 2, 8, 10, 1, 7, 4, 4, 7, 1, 10, 12, 0, 9, 3, 6, 6, 3, 9, 0, 12, 11, 2, 8, 5, 5, 8, 2, 11, 13, 1, 10, 4, 7, 7, 4, 10, 1, 13, 15, 0, 12, 3, 9, 6, 6

Offset: 2

Author

Florentin Smarandache (smarand(AT)unm.edu), Nov 03 2010

Keywords

• nonn
• easy
• tabf
• less

Comments

Row lengths are 2*A008611(n). Row sums are n*A008611(n).- R. J. Mathar, May 13 2016

Examples

			1, 1;
3, 0, 0, 3;
2, 2;
4, 1, 1, 4;
6, 0, 3, 3, 0, 6;
5, 2, 2, 5;
7, 1, 4, 4, 1, 7;
9, 0, 6, 3, 3, 6, 0, 9;
8, 2, 5, 5, 2, 8;
10, 1, 7, 4, 4, 7, 1, 10;
12, 0, 9, 3, 6, 6, 3, 9, 0, 12;
11, 2, 8, 5, 5, 8, 2, 11;
13, 1, 10, 4, 7, 7, 4, 10, 1, 13;
15, 0, 12, 3, 9, 6, 6, 9, 3, 12, 0, 15;
14, 2, 11, 5, 8, 8, 5, 11, 2, 14;
		

Programs

Maple

A181634_row := proc(n)
    local L,a,b;
    L := [] ;
    for a from n to 0 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:
for n from 2 to 18 do
    print(op(A181634_row(n))) ;
end do: # R. J. Mathar, May 13 2016

Mathematica

If[First@ # == Last@ # &@ Take[#, 2], Join[Reverse@ Drop[#, 2], #], Join[Reverse@ #, #]] & /@ Function[n, Flatten@ Select[Transpose@ {n - #, #}, Mod[First@ #, 3] == Mod[Last@ #, 3] &] &@ Range[Ceiling[n/2], n]] /@ Range[2, 16] // Flatten (* Michael De Vlieger, May 13 2016 *)

Extensions

Edited by R. J. Mathar, May 13 2016