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A342708
Triangle read by rows with n >= 1, 0 <= k <= n-1: in general T(n,k) = T(n-1,k-1) - T(n-k,k), except T(1,0)=1, T(n,0)=0 for n>=2; T(n,k) = 0 for k>=n.
1
1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, -1, 0, -1, 1, 0, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, -1, 1, 0, 1, -1, 2, -1, 0, -1, 1, 0, -1, 0, -1, 1, -1, 0, -1, 1, 0, 1, 0, 1, 0, 1, -1, 0, -1, 1, 0, -1, 1, -2, 1, -1, 1, -1, 0, -1, 1, 0, 1, -1, 2, -1, 2, -1, 1, -1, 0, -1, 1
OFFSET
1,32
COMMENTS
Absolute value of sum of triangle array rows = A000700.
Sum of absolute value of each number in a row = absolute value of A000025.
Triangle recurrence is the same as A008284 (row sums equal A000041) except instead of adding the two pieces for the corresponding output a subtraction is performed.
LINKS
Joe Michelson, Table of n, a(n) for n = 1..11628 (first 152 rows)
EXAMPLE
The triangle begins:
.
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 ...
---+--------------------------------------------------
1 | 1;
2 | 0, 1;
3 | 0, -1, 1;
4 | 0, 1, -1, 1;
5 | 0, -1, 0, -1, 1;
6 | 0, 1, 0, 0, -1, 1;
7 | 0, -1, 1, -1, 0, -1, 1;
8 | 0, 1, -1, 2, -1, 0, -1, 1;
9 | 0, -1, 0, -1, 1, -1, 0, -1, 1;
10 | 0, 1, 0, 1, 0, 1, -1, 0, -1, 1;
11 | 0, -1, 1, -2, 1, -1, 1, -1, 0, -1, 1;
12 | 0, 1, -1, 2, -1, 2, -1, 1, -1, 0, -1, 1;
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Joe Michelson, Mar 18 2021
STATUS
approved