Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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