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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. 5

%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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Last modified April 21 02:41 EDT 2021. Contains 343143 sequences. (Running on oeis4.)