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A185911
Weight array of A185910, by antidiagonals.
4
1, 1, 3, 1, 0, 5, 1, 0, 0, 7, 1, 0, 0, 0, 9, 1, 0, 0, 0, 0, 11, 1, 0, 0, 0, 0, 0, 13, 1, 0, 0, 0, 0, 0, 0, 15, 1, 0, 0, 0, 0, 0, 0, 0, 17, 1, 0, 0, 0, 0, 0, 0, 0, 0, 19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27
OFFSET
1,3
COMMENTS
A member of the accumulation chain ... < A185910 < A185911 < A185912 < A185913 < ...
(See A144112 for definitions of weight array and accumulation array.)
FORMULA
T(1,k) = 1 for k >= 1; T(n,1) = 2*n-1 for n >= 1; T(n,k) = 0 otherwise.
EXAMPLE
Northwest corner:
1, 1, 1, 1, 1, 1
3, 0, 0, 0, 0, 0
5, 0, 0, 0, 0, 0
7, 0, 0, 0, 0, 0
9, 0, 0, 0, 0, 0
MATHEMATICA
f[n_, 0] := 0; f[0, k_] := 0; f[n_, k_] := n^2 + k - 1;
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
T[1, k_] := 1; T[n_, 1] := 2*n - 1; T[n_, k_] := 0; Table[T[n - k + 1, k], {n, 10}, {k, n, 1, -1}]//Flatten (* G. C. Greubel, Jul 22 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 06 2011
STATUS
approved