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%I
%S 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 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 11,7,4,2,1,23,17,12,8,5,3,24,18,13,9,6,25,19,14
%N 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 Peter Kagey, <a href="/A273823/b273823.txt">Table of n, a(n) for n = 1..10000</a>
%e A000027 read by antidiagonals is:
%e 1 2 4 7
%e 3 5 8
%e 6 9
%e ...
%e Thus:
%e Row 1: []
%e Row 2: [1]
%e Row 3: []
%e Row 4: [2, 1]
%e Row 5: [3]
%e Row 6: []
%e Row 7: [4, 2, 1]
%e Row 8: [5, 3]
%e Row 9: [6]
%t 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 (Haskell)
%o a273823 n = genericIndex a273823_list (n - 1)
%o a273823_list = concatMap a273823_row [1..]
%o a273823_tabf = map a273823_row [1..]
%o a273823_row n
%o | a_i == 0 = []
%o | otherwise = a_i : a273823_row a_i where
%o a_i = a271439 n
%Y Cf. A000027, A025581 (row length), A269526, A271439, A273824, A273825, A274079, A274080.
%K nonn,tabf,look
%O 1,2
%A _Peter Kagey_, Jun 08 2016
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