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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
OFFSET
1
COMMENTS
A member of the accumulation chain ... < A185916 < A185914 < A185915 < ...
(See A144112 for definitions of weight array and accumulation array.)
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
KEYWORD
tabl,sign
AUTHOR
Clark Kimberling, Feb 06 2011
STATUS
approved