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.

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, 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, 11, 7, 4, 2, 1, 23, 17, 12, 8, 5, 3, 24, 18, 13, 9, 6, 25, 19, 14

Offset

1,2

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Example

A000027 read by antidiagonals is:
1 2 4 7
3 5 8
6 9
...
Thus:
Row 1: []
Row 2: [1]
Row 3: []
Row 4: [2, 1]
Row 5: [3]
Row 6: []
Row 7: [4, 2, 1]
Row 8: [5, 3]
Row 9: [6]

Mathematica

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 *)

Prog

(Haskell)
a273823 n = genericIndex a273823_list (n - 1)
a273823_list = concatMap a273823_row [1..]
a273823_tabf = map a273823_row [1..]
a273823_row n
  | a_i == 0  = []
  | otherwise = a_i : a273823_row a_i where
    a_i = a271439 n

Crossrefs

Cf. A000027, A025581 (row length), A269526, A271439, A273824, A273825, A274079, A274080.

Sequence in context: A341231 A334081 A125158 * A112384 A248514 A123390

Adjacent sequences: A273820 A273821 A273822 * A273824 A273825 A273826

Keyword

nonn,tabf,look

Author

Peter Kagey, Jun 08 2016

Status

approved