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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.

%I A286100 #28 Dec 14 2024 04:00:20
%S A286100 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 A286100 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 A286100 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 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.
%H A286100 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 A286100 If n = k, then A(n,k) = n, otherwise 0.
%e A286100 The top left 9 X 9 corner of the array:
%e A286100   1, 0, 0, 0, 0, 0, 0, 0, 0
%e A286100   0, 2, 0, 0, 0, 0, 0, 0, 0
%e A286100   0, 0, 3, 0, 0, 0, 0, 0, 0
%e A286100   0, 0, 0, 4, 0, 0, 0, 0, 0
%e A286100   0, 0, 0, 0, 5, 0, 0, 0, 0
%e A286100   0, 0, 0, 0, 0, 6, 0, 0, 0
%e A286100   0, 0, 0, 0, 0, 0, 7, 0, 0
%e A286100   0, 0, 0, 0, 0, 0, 0, 8, 0
%e A286100   0, 0, 0, 0, 0, 0, 0, 0, 9
%t A286100 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 A286100 (Scheme)
%o A286100 (define (A286100 n) (A286100bi (A002260 n) (A004736 n)))
%o A286100 (define (A286100bi row col) (if (= row col) row 0))
%o A286100 (Python)
%o A286100 def A(n, k): return n if n==k else 0
%o A286100 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 A286100 Cf. A000027 (the main diagonal).
%Y A286100 Cf. also arrays A003982, A285732.
%K A286100 nonn,tabl
%O A286100 1,5
%A A286100 _Antti Karttunen_, May 03 2017