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

2,3

Comments

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

Links

Table of n, a(n) for n=2..86.

Example

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;

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 *)

Crossrefs

Sequence in context: A359967 A284281 A075874 * A230652 A230661 A178952

Adjacent sequences: A181631 A181632 A181633 * A181635 A181636 A181637

Keyword

nonn,easy,tabf,less

Author

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

Extensions

Edited by R. J. Mathar, May 13 2016

Status

approved