A185911 - OEIS

%I #14 Jul 22 2017 09:15:24

%S 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,

%T 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,

%U 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

%N Weight array of A185910, by antidiagonals.

%C A member of the accumulation chain ... < A185910 < A185911 < A185912 < A185913 < ...

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

%H G. C. Greubel, <a href="/A185911/b185911.txt">Table of n, a(n) for the first 50 rows, flattened</a>

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

%e Northwest corner:

%e   1, 1, 1, 1, 1, 1

%e   3, 0, 0, 0, 0, 0

%e   5, 0, 0, 0, 0, 0

%e   7, 0, 0, 0, 0, 0

%e   9, 0, 0, 0, 0, 0

%t f[n_, 0] := 0; f[0, k_] := 0; f[n_, k_] := n^2 + k - 1;

%t w[m_, n_] := f[m, n] + f[m - 1, n - 1] - f[m, n - 1] - f[m - 1, n] /; Or[m > 0, n > 0];

%t Table[w[n - k + 1, k], {n, 50}, {k, n, 1, -1}] // Flatten

%t 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 *)

%Y Cf. A144112, A185910, A185912.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Feb 06 2011