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A177978
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Triangle T(n,k) read by rows: A051731(n,k) - A051731(n-1,k).
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2
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The recurrence for this triangle is similar to the recurrence in A177517. Cumulative column sums give table A051731.
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LINKS
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FORMULA
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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)).
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EXAMPLE
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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;
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PROG
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(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))
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Typo in sequence (erroneous comma) corrected by N. J. A. Sloane, May 22 2010
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STATUS
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approved
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