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A185907 Weight array of A185908, by antidiagonals. 4
1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

A member of the accumulation chain ... < A185907 < A185908 < A185909 < ...

(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

All entries in column 1 and main diagonal are 1, all others are 0.

EXAMPLE

Northwest corner:

  1, 0, 0, 0, 0, 0, 0, 0

  1, 1, 0, 0, 0, 0, 0, 0

  1, 0, 1, 0, 0, 0, 0, 0

  1, 0, 0, 1, 0, 0, 0, 0

  1, 0, 0, 0, 1, 0, 0, 0

MATHEMATICA

(* This program generates the array A185908, then its accumulation array, A185909, and then its weight array, A185907. *)

f[n_, 0]:=0; f[0, k_]:=0;  (* needed for the weight array *)

f[n_, k_]:=Min[n, k]+n-1;

TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]

Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

s[n_, k_]:=Sum[f[i, j], {i, 1, n}, {j, 1, k}]; (* accumulation array of {f(n, k)} *)

TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]  (* A185909 *)]

Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

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

TableForm[Table[w[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185907 *)

Table[w[n-k+1, k], {n, 16}, {k, n, 1, -1}]//Flatten

CROSSREFS

Cf. A144112, A185908, A185909.

Sequence in context: A131483 A077052 A133566 * A321016 A077051 A115955

Adjacent sequences:  A185904 A185905 A185906 * A185908 A185909 A185910

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 06 2011

STATUS

approved

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Last modified May 12 10:54 EDT 2021. Contains 343821 sequences. (Running on oeis4.)