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

1,4

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.

Links

Table of n, a(n) for n=1..105.

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)).

Example

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;

Prog

(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))

Crossrefs

Cf. A179286, A179287, A059571, A051731.

Sequence in context: A306722 A168508 A177994 * A079211 A026835 A117975

Adjacent sequences: A179282 A179283 A179284 * A179286 A179287 A179288

Keyword

nonn,tabl

Author

Mats Granvik, Jul 09 2010

Status

approved