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, 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

Cf. A000700, A000025, A008284, A072233.

Sequence in context: A259896 A337086 A113313 * A074871 A182641 A337939

Adjacent sequences: A342705 A342706 A342707 * A342709 A342710 A342711

Keyword

sign,tabl

Author

Joe Michelson, Mar 18 2021

Status

approved