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%I #12 Feb 26 2019 23:05:32
%S 1,1,2,1,0,2,1,2,-2,2,1,0,2,-2,2,1,2,0,0,-2,2,1,0,0,2,0,-2,2,1,2,0,0,
%T 0,0,-2,2,1,0,2,-2,2,0,0,-2,2,1,2,-2,2,0,0,0,0,-2,2,1,0,2,0,-2,2,0,0,
%U 0,-2,2,1,2,0,0,0,0,0,0,0,0,-2,2,1,0,0,0,2,-2,2,0,0,0,0,-2,2,1,2,0,0,0,0,0,0
%N Triangle T(n,k) defined by the recurrence in the formula.
%F T(n,1)=1. T(n,2) = 2-T(n-1,2). T(n,k) = Sum_{i=1..k-2} T(n-i,k-1) - Sum{i=1..k-1} T(n-i,k) for k > 2.
%e Table starts:
%e 1;
%e 1, 2;
%e 1, 0, 2;
%e 1, 2, -2, 2;
%e 1, 0, 2, -2, 2;
%e 1, 2, 0, 0, -2, 2;
%e 1, 0, 0, 2, 0, -2, 2;
%e 1, 2, 0, 0, 0, 0, -2, 2;
%e 1, 0, 2, -2, 2, 0, 0, -2, 2;
%e 1, 2, -2, 2, 0, 0, 0, 0, -2, 2;
%p A180430 := proc(n,k) option remember; if k>n then 0; elif k = 1 then 1; elif k = 2 then 2-procname(n-1,k) ; else add( procname(n-i,k-1),i=1..k-2) - add(procname(n-i,k),i=1..k-1) ; end if; end proc: # _R. J. Mathar_, Jul 13 2011
%o (Excel) Using European dot comma style:
%o =if(column()=1; 1; if(row()>=column(); sum(indirect(address(row()-column()+2; column()-1; 4)&":"&address(row()-1; column()-1; 4); 4))-sum(indirect(address(row()-column()+1; column(); 4)&":"&address(row()-1; column(); 4); 4)); 0))
%Y Cf. A176702.
%K sign,tabl
%O 1,3
%A _Mats Granvik_, Sep 04 2010
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