A185917 Weight array of max{n,k}, by antidiagonals.

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

Offset

1

Comments

A member of the accumulation chain ... < A185917 < A051125 < A185958 < ..., where A051125, written as a rectangular array M, is given by M(n,k) = max{n,k}. See A144112 for definitions of weight array and accumulation array.

Equals A115359 when the first row of the array is removed. - Georg Fischer, Jul 26 2023

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Formula

T(n,k)= 1 if n=1 or k=1; T(n,n)= -1 for n>1; T(n,k)= 0 otherwise.

Example

Northwest corner:
  1,  1,  1,  1,  1,  1
  1, -1,  0,  0,  0,  0
  1,  0, -1,  0,  0,  0
  1,  0,  0, -1,  0,  0
  1,  0,  0,  0, -1,  0

Mathematica

T[1, k_] := 1; T[n_, 1] := 1; T[n_, n_] := -1; T[n_, k_] := 0;
TableForm[Table[T[n, k], {n, 1, 5}, {k, 1, 5}]]
Table[T[n - k + 1, k], {n, 10}, {k, n, 1, -1}] (* G. C. Greubel, Jul 22 2017 *)

Crossrefs

Cf. A051125, A115359, A144112.

Sequence in context: A166360 A204183 A204177 * A143104 A127236 A117947

Adjacent sequences: A185914 A185915 A185916 * A185918 A185919 A185920

Keyword

tabl,sign

Author

Clark Kimberling, Feb 07 2011

Status

approved