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A177978
Triangle T(n,k) read by rows: A051731(n,k) - A051731(n-1,k).
2
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.
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
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