A180430 Triangle T(n,k) defined by the recurrence in the formula.

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, 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, 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

Offset: 1

Author

Mats Granvik, Sep 04 2010

Keywords

• sign
• tabl

Examples

			Table starts:
  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,  0,  0, -2,  2;
  1,  0,  2, -2,  2,  0,  0, -2,  2;
  1,  2, -2,  2,  0,  0,  0,  0, -2,  2;
		

Crossrefs

Cf. A176702.

Programs

Excel

Using European dot comma style:
=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))

Maple

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

Formula

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.