login
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.
4

%I #28 Dec 14 2024 04:00:20

%S 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,

%T 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,

%U 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

%N 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.

%H Antti Karttunen, <a href="/A286100/b286100.txt">Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of the array</a>

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

%e The top left 9 X 9 corner of the array:

%e 1, 0, 0, 0, 0, 0, 0, 0, 0

%e 0, 2, 0, 0, 0, 0, 0, 0, 0

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

%e 0, 0, 0, 4, 0, 0, 0, 0, 0

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

%e 0, 0, 0, 0, 0, 6, 0, 0, 0

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

%e 0, 0, 0, 0, 0, 0, 0, 8, 0

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

%t 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 *)

%o (Scheme)

%o (define (A286100 n) (A286100bi (A002260 n) (A004736 n)))

%o (define (A286100bi row col) (if (= row col) row 0))

%o (Python)

%o def A(n, k): return n if n==k else 0

%o for n in range(1, 21): print( [A(k, n - k + 1) for k in range(1, n + 1)] ) # _Indranil Ghosh_, May 03 2017

%Y Cf. A000027 (the main diagonal).

%Y Cf. also arrays A003982, A285732.

%K nonn,tabl

%O 1,5

%A _Antti Karttunen_, May 03 2017