A181634 - OEIS

%I #19 Nov 08 2016 19:49:33

%S 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,

%T 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,

%U 2,11,13,1,10,4,7,7,4,10,1,13,15,0,12,3,9,6,6

%N 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).

%C Row lengths are 2*A008611(n). Row sums are n*A008611(n).- _R. J. Mathar_, May 13 2016

%e 1, 1;

%e 3, 0, 0, 3;

%e 2, 2;

%e 4, 1, 1, 4;

%e 6, 0, 3, 3, 0, 6;

%e 5, 2, 2, 5;

%e 7, 1, 4, 4, 1, 7;

%e 9, 0, 6, 3, 3, 6, 0, 9;

%e 8, 2, 5, 5, 2, 8;

%e 10, 1, 7, 4, 4, 7, 1, 10;

%e 12, 0, 9, 3, 6, 6, 3, 9, 0, 12;

%e 11, 2, 8, 5, 5, 8, 2, 11;

%e 13, 1, 10, 4, 7, 7, 4, 10, 1, 13;

%e 15, 0, 12, 3, 9, 6, 6, 9, 3, 12, 0, 15;

%e 14, 2, 11, 5, 8, 8, 5, 11, 2, 14;

%p A181634_row := proc(n)

%p     local L,a,b;

%p     L := [] ;

%p     for a from n to 0 by -1 do

%p         b := n-a ;

%p         if modp(a,3) = modp(b,3) then

%p             L := [op(L),a,b] ;

%p         end if;

%p     end do:

%p     L ;

%p end proc:

%p for n from 2 to 18 do

%p     print(op(A181634_row(n))) ;

%p end do: # _R. J. Mathar_, May 13 2016

%t 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 *)

%K nonn,easy,tabf,less

%O 2,3

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

%E Edited by _R. J. Mathar_, May 13 2016