A179285 Triangle T(n,k) read by rows, defined by: T(1,1)=1; n > 1 and k=1: T(n,1) = T(n-1,2) + T(n,2); k=2: T(n,2) = A000196(n-1); k > 2: T(n,k) = (Sum_{i=1..k-1} T(n-i,k-1)) - (Sum_{i=1..k-1} T(n-i,k)).

1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 2, 0, 1, 1, 4, 2, 2, 0, 1, 1, 4, 2, 2, 1, 0, 1, 1, 4, 2, 0, 2, 1, 0, 1, 1, 4, 2, 2, 1, 1, 1, 0, 1, 1, 5, 3, 2, 0, 1, 1, 1, 0, 1, 1, 6, 3, 1, 1, 1, 0, 1, 1, 0, 1, 1, 6, 3, 3, 3, 0, 1, 0, 1, 1, 0, 1, 1, 6, 3, 2, 2, 2, 1, 0, 0, 1, 1, 0, 1, 1, 6, 3, 1, 0, 2, 1, 1, 0, 0, 1, 1, 0, 1, 1

Offset: 1

Author

Mats Granvik, Jul 09 2010

Keywords

• nonn
• tabl

Comments

The second column, sequence A000196, is the initial condition for the recurrence in this triangle. See A051731, formula entered on Feb 16 2010 for the more pure form of this recurrence.

Examples

			Triangle begins:
  1;
  1, 1;
  2, 1, 1;
  2, 1, 1, 1;
  3, 2, 0, 1, 1;
  4, 2, 2, 0, 1, 1;
  4, 2, 2, 1, 0, 1, 1;
  4, 2, 0, 2, 1, 0, 1, 1;
  4, 2, 2, 1, 1, 1, 0, 1, 1;
  5, 3, 2, 0, 1, 1, 1, 0, 1, 1;
  6, 3, 1, 1, 1, 0, 1, 1, 0, 1, 1;
		

Crossrefs

Cf. A179286, A179287, A059571, A051731.

Programs

Excel

Using European dot comma style:
=if(and(row()=1;column()=1);1;if(row()>=column();if(column()=1;indirect(address(row()-1;column()+1))+indirect(address(row();column()+1));if(column()=2;floor(((row()-1)^0,5);1);if(row()>=column();sum(indirect(address(row()-column()+1;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)));0))

Formula

T(1,1)=1; n > 1 and k=1: T(n,1) = T(n-1,2) + T(n,2); k=2: T(n,2) = A000196(n-1); k > 2: T(n,k) = (Sum_{i=1..k-1} T(n-i,k-1)) - (Sum_{i=1..k-1} T(n-i,k)).