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A185916 Weight array of A185914, by antidiagonals. 3
1, 1, -1, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

A member of the accumulation chain ... < A185916 < A185914 < A185915 < ...

(See A144112 for definitions of weight array and accumulation array.)

LINKS

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

FORMULA

T(1,k)=1 for k>=1; T(n,n+1)=-1 for n>=2; T(n,k)=0 otherwise; for k>=1, n>=1.

EXAMPLE

Northwest corner:

   1,  1,  1,  1,  1,  1,  1

  -1,  0,  0,  0,  0,  0,  0

   0, -1,  0,  0,  0,  0,  0

   0,  0, -1,  0,  0,  0,  0

   0,  0,  0, -1,  0,  0,  0

   0,  0,  0,  0, -1,  0,  0

MATHEMATICA

f[n_, 0] := 0; f[0, k_] := 0; f[n_, k_] := k - n + 1; f[n_, k_] := 0 /; k < n; w[m_, n_] := f[m, n] + f[m - 1, n - 1] - f[m, n - 1] - f[m - 1, n] /; Or[m > 0, n > 0]; Table[w[n - k + 1, k], {n, 50}, {k, n, 1, -1}] // Flatten

CROSSREFS

Cf. A115359, A144112, A185914, A185915.

Sequence in context: A131078 A302203 A130657 * A084846 A285498 A285504

Adjacent sequences:  A185913 A185914 A185915 * A185917 A185918 A185919

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Feb 06 2011

STATUS

approved

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Last modified March 29 18:26 EDT 2020. Contains 333116 sequences. (Running on oeis4.)