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A273823 Table read by rows: the n-th row is the list of numbers to the left of n in the natural numbers read by antidiagonals.

%I A273823 #22 Jul 02 2016 22:54:49
%S A273823 1,2,1,3,4,2,1,5,3,6,7,4,2,1,8,5,3,9,6,10,11,7,4,2,1,12,8,5,3,13,9,6,
%T A273823 14,10,15,16,11,7,4,2,1,17,12,8,5,3,18,13,9,6,19,14,10,20,15,21,22,16,
%U A273823 11,7,4,2,1,23,17,12,8,5,3,24,18,13,9,6,25,19,14
%N A273823 Table read by rows: the n-th row is the list of numbers to the left of n in the natural numbers read by antidiagonals.
%H A273823 Peter Kagey, <a href="/A273823/b273823.txt">Table of n, a(n) for n = 1..10000</a>
%e A273823 A000027 read by antidiagonals is:
%e A273823 1 2 4 7
%e A273823 3 5 8
%e A273823 6 9
%e A273823 ...
%e A273823 Thus:
%e A273823 Row 1: []
%e A273823 Row 2: [1]
%e A273823 Row 3: []
%e A273823 Row 4: [2, 1]
%e A273823 Row 5: [3]
%e A273823 Row 6: []
%e A273823 Row 7: [4, 2, 1]
%e A273823 Row 8: [5, 3]
%e A273823 Row 9: [6]
%t A273823 nn = 32; t = Table[(n^2 - n)/2 + Accumulate@ Range[n - 1, Ceiling[(Sqrt[9 + 8 nn] - 3)/2]] + 1, {n, Ceiling[(Sqrt[9 + 8 nn] - 3)/2] + 1}]; Table[Reverse@ Take[t[[#1]], #2 - 1] & @@ Flatten@ Position[t, n], {n, nn}] // Flatten (* _Michael De Vlieger_, Jun 10 2016 *)
%o A273823 (Haskell)
%o A273823 a273823 n = genericIndex a273823_list (n - 1)
%o A273823 a273823_list = concatMap a273823_row [1..]
%o A273823 a273823_tabf = map a273823_row [1..]
%o A273823 a273823_row n
%o A273823   | a_i == 0  = []
%o A273823   | otherwise = a_i : a273823_row a_i where
%o A273823     a_i = a271439 n
%Y A273823 Cf. A000027, A025581 (row length), A269526, A271439, A273824, A273825, A274079, A274080.
%K A273823 nonn,tabf,look
%O A273823 1,2
%A A273823 _Peter Kagey_, Jun 08 2016