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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A049711 A137293 A177803 * A074641 A069003 A087855

Adjacent sequences:  A274077 A274078 A274079 * A274081 A274082 A274083

KEYWORD

nonn,tabf,look

AUTHOR

Peter Kagey, Jun 09 2016

STATUS

approved

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Last modified April 23 07:37 EDT 2021. Contains 343201 sequences. (Running on oeis4.)