

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, 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
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OFFSET

2,3


COMMENTS



LINKS



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

local L, a, b;
L := [] ;
for a from n to 0 by 1 do
b := na ;
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


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



KEYWORD

nonn,easy,tabf,less


AUTHOR

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


EXTENSIONS



STATUS

approved



