A286100 Square array A(n,k): If n = k, then A(n,k) = n, otherwise 0, read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0

Offset

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of the array

Formula

If n = k, then A(n,k) = n, otherwise 0.

Example

The top left 9 X 9 corner of the array:
  1, 0, 0, 0, 0, 0, 0, 0, 0
  0, 2, 0, 0, 0, 0, 0, 0, 0
  0, 0, 3, 0, 0, 0, 0, 0, 0
  0, 0, 0, 4, 0, 0, 0, 0, 0
  0, 0, 0, 0, 5, 0, 0, 0, 0
  0, 0, 0, 0, 0, 6, 0, 0, 0
  0, 0, 0, 0, 0, 0, 7, 0, 0
  0, 0, 0, 0, 0, 0, 0, 8, 0
  0, 0, 0, 0, 0, 0, 0, 0, 9

Mathematica

Table[Function[s, If[OddQ@ Length@ s, ReplacePart[s, {# -> #}] &[Ceiling[n/2]], s]]@ ConstantArray[0, n], {n, 15}] // Flatten (* Michael De Vlieger, May 04 2017 *)

Prog

(Scheme)
(define (A286100 n) (A286100bi (A002260 n) (A004736 n)))
(define (A286100bi row col) (if (= row col) row 0))
(Python)
def A(n, k): return n if n==k else 0
for n in range(1, 21): print [A(k, n - k + 1) for k in range(1, n + 1)] # Indranil Ghosh, May 03 2017

Crossrefs

Cf. A000027 (the main diagonal).

Cf. also arrays A003982, A285732.

Sequence in context: A028702 A083929 A182660 * A359431 A338210 A122698

Adjacent sequences: A286097 A286098 A286099 * A286101 A286102 A286103

Keyword

nonn,tabl

Author

Antti Karttunen, May 03 2017

Status

approved