A274080 Table read by rows: row n gives all numbers less than n in the same row, column, or diagonal as n in the natural numbers read by antidiagonals.

1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 3, 4, 5, 1, 2, 4, 2, 3, 4, 5, 7, 2, 3, 5, 6, 7, 8, 1, 3, 6, 7, 8, 9, 1, 2, 4, 7, 3, 4, 5, 7, 8, 11, 1, 4, 5, 6, 8, 9, 11, 12, 2, 5, 6, 9, 10, 11, 12, 13, 1, 3, 6, 10, 11, 12, 13, 14, 1, 2, 4, 7, 11, 3, 5, 7, 8, 11, 12, 16, 2, 6, 7

Offset

1,3

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: [1, 2]
Row 4: [1, 2]
Row 5: [1, 2, 3, 4]
Row 6: [1, 3, 4, 5]
Row 7: [1, 2, 4]
Row 8: [2, 3, 4, 5, 7]
Row 9: [2, 3, 5, 6, 7, 8]

Mathematica

nn = 18; 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[Function[a, Function[p, Most@ Union@ Flatten@ {Map[a[[#1, #2]] & @@ # &, Most@ NestWhileList[# - 1 &, First@ p, ! MemberQ[#, 0] &]], Range[SelectFirst[Reverse@ Join[{0}, First@ t], n >= # &], n - 1], Transpose[a][[ p[[1, 2]] ]], a[[ p[[1, 1]] ]]}]@ Position[a, n]]@ Array[t[[#1, #2]] &, First@ Position[t, n]], {n, nn}] // Flatten (* Michael De Vlieger, Jun 29 2016, Version 10 *)

Prog

(Haskell)
import Data.List (sort, nub)
a274080 n = a274080_list !! (n - 1)
a274080_list = concatMap a274080_row [1..]
a274080_tabf = map a274080_row [1..]
a274080_row n = nub $ sort $ concatMap (\f -> f n) [a274079_row, a273825_row, a273824_row, a273823_row]

Crossrefs

Cf. A000027, A269526, A273823, A273824, A273825, A274079.

Sequence in context: A137293 A366254 A177803 * A074641 A069003 A087855

Adjacent sequences: A274077 A274078 A274079 * A274081 A274082 A274083

Keyword

nonn,tabf,look

Author

Peter Kagey, Jun 09 2016

Status

approved