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%I #20 Jun 30 2016 02:01:56
%S 1,2,3,4,5,1,6,7,8,2,9,3,10,11,12,4,13,5,1,14,6,15,16,17,7,18,8,2,19,
%T 9,3,20,10,21,22,23,11,24,12,4,25,13,5,1,26,14,6,27,15,28,29,30,16,31,
%U 17,7,32,18,8,2,33,19,9,3,34,20,10,35,21,36,37,38,22
%N Table read by rows: the n-th row is the list of numbers diagonally up and to the left of n in the natural numbers read by antidiagonals.
%H Peter Kagey, <a href="/A273825/b273825.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: []
%e Row 3: []
%e Row 4: []
%e Row 5: [1]
%e Row 6: []
%e Row 7: []
%e Row 8: [2]
%e Row 9: [3]
%t nn = 58; 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[Rest@ Map[t[[#1, #2]] & @@ # &, Most@ NestWhileList[# - 1 &, #, ! MemberQ[#, 0] &]] &@ First@ Position[t, n], {n, nn}] // Flatten (* _Michael De Vlieger_, Jun 29 2016 *)
%o (Haskell)
%o a273825 n = genericIndex a273825_list (n - 1)
%o a273825_list = concatMap a273825_row [1..]
%o a273825_tabf = map a273825_row [1..]
%o a273825_row n
%o | a_i == 0 = []
%o | otherwise = a_i : a273825_row a_i where
%o a_i = a271439 $ a271439 (n - 1)
%Y Cf. A000027, A269526, A271439, A273823, A273824, A274079, A274080.
%K nonn,tabf
%O 1,2
%A _Peter Kagey_, Jun 08 2016
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