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

Author

Antti Karttunen, May 03 2017

Keywords

• nonn
• tabl

Examples

			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
		

Links

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

Crossrefs

Cf. A000027 (the main diagonal).

Cf. also arrays A003982, A285732.

Programs

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 *)

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

Scheme

(define (A286100 n) (A286100bi (A002260 n) (A004736 n)))
(define (A286100bi row col) (if (= row col) row 0))

Formula

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