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A112367 a(n) = A000217(n-k), where k is the largest triangular number less than n.

%I A112367 #9 Aug 09 2015 00:50:44
%S A112367 0,0,1,0,1,3,0,1,3,6,0,1,3,6,10,0,1,3,6,10,15,0,1,3,6,10,15,21,0,1,3,
%T A112367 6,10,15,21,28,0,1,3,6,10,15,21,28,36,0,1,3,6,10,15,21,28,36,45,0,1,3,
%U A112367 6,10,15,21,28,36,45,55,0,1,3,6,10
%N A112367 a(n) = A000217(n-k), where k is the largest triangular number less than n.
%F A112367 a(n) = A000217(n-A057944(n)). - _R. J. Mathar_, Nov 05 2011
%e A112367 a(9) = T(9-6) = T(3) = 6. 6 < 9 < 10.
%p A112367 A112367 := proc(n)
%p A112367         t := A057944(n) ;
%p A112367         A000217(n-t) ;
%p A112367 end proc:
%p A112367 seq(A112367(n),n=0..80) ; # _R. J. Mathar_, Nov 05 2011
%t A112367 trn[n_]:=Module[{c=Floor[(Sqrt[8n+1]-1)/2],x},x=n-(c(c+1))/2;(x(x+1))/2]; Array[trn,80,0] (* _Harvey P. Dale_, Jul 19 2012 *)
%K A112367 easy,nonn
%O A112367 0,6
%A A112367 _Amarnath Murthy_, Sep 12 2005