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A273824 Table read by rows: the n-th row is the list of numbers above n in the table of natural numbers read by antidiagonals.

%I A273824 #20 Jul 02 2016 22:55:02
%S A273824 1,2,3,1,4,5,2,6,3,1,7,8,4,9,5,2,10,6,3,1,11,12,7,13,8,4,14,9,5,2,15,
%T A273824 10,6,3,1,16,17,11,18,12,7,19,13,8,4,20,14,9,5,2,21,15,10,6,3,1,22,23,
%U A273824 16,24,17,11,25,18,12,7,26,19,13,8,4,27,20,14,9,5
%N A273824 Table read by rows: the n-th row is the list of numbers above n in the table of natural numbers read by antidiagonals.
%H A273824 Peter Kagey, <a href="/A273824/b273824.txt">Table of n, a(n) for n = 1..10000</a>
%e A273824 A000027 read by antidiagonals is:
%e A273824 1 2 4 7
%e A273824 3 5 8
%e A273824 6 9
%e A273824 ...
%e A273824 Thus:
%e A273824 Row 1: []
%e A273824 Row 2: []
%e A273824 Row 3: [1]
%e A273824 Row 4: []
%e A273824 Row 5: [2]
%e A273824 Row 6: [3, 1]
%e A273824 Row 7: []
%e A273824 Row 8: [4]
%e A273824 Row 9: [5, 2]
%t A273824 nn = 35; t = Transpose@ Table[(n^2 - n)/2 + Accumulate@ Range[n - 1, n + 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 A273824 (Haskell)
%o A273824 a273824 n = genericIndex a273824_list (n - 1)
%o A273824 a273824_list = concatMap a273824_row [1..]
%o A273824 a273824_tabf = map a273824_row [1..]
%o A273824 a273824_row n
%o A273824   | a_i == 0  = []
%o A273824   | otherwise = a_i : a273824_row a_i where
%o A273824     a_i = a271439 (n - 1)
%Y A273824 Cf. A000027, A269526, A271439, A273823, A273825, A274079, A274080.
%K A273824 nonn,tabf
%O A273824 1,2
%A A273824 _Peter Kagey_, Jun 08 2016