A177978 Triangle T(n,k) read by rows: A051731(n,k) - A051731(n-1,k).

1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, -1, 0, -1, 1, 0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 0, -1, 1, 0, 1, 0, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, 0, 0, -1, 1, 0, 1, -1, 0, 1, 0, 0, 0, -1, 1, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, -1, 1, 0, -1, -1, -1, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 1

Offset

1,1

Comments

The recurrence for this triangle is similar to the recurrence in A177517. Cumulative column sums give table A051731.

Links

Table of n, a(n) for n=1..93.

Formula

T(n,1)=A000007, k > 1: 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;
  0,  1;
  0, -1,  1;
  0,  1, -1,  1;
  0, -1,  0, -1,  1;
  0,  1,  1,  0, -1,  1;
  0, -1, -1,  0,  0, -1,  1;
  0,  1,  0,  1,  0,  0, -1,  1;
  0, -1,  1, -1,  0,  0,  0, -1,  1;
  0,  1, -1,  0,  1,  0,  0,  0, -1,  1;
  0, -1,  0,  0, -1,  0,  0,  0,  0, -1,  1;
  0,  1,  1,  1,  0,  1,  0,  0,  0,  0, -1,  1;
  0, -1, -1, -1,  0, -1,  0,  0,  0,  0,  0, -1,  1;
  0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  0,  0, -1,  1;

Prog

(Excel cell formula, American) =if(column()=1, if(row()>1, 0, 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))
(Excel cell formula, European)=if(column()=1; if(row()>1; 0; 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))

Crossrefs

Matrix inverse of A134540. Cf. A177517.

Sequence in context: A114483 A127822 A111967 * A213061 A110247 A114607

Adjacent sequences: A177975 A177976 A177977 * A177979 A177980 A177981

Keyword

sign,tabl

Author

Mats Granvik, May 16 2010

Extensions

Typo in sequence (erroneous comma) corrected by N. J. A. Sloane, May 22 2010

Edited by Mats Granvik, Dec 11 2010

Status

approved