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 A026793 Juxtaposed partitions of 1,2,3,... into distinct parts, ordered by number of terms and then lexicographically. 17
 1, 2, 3, 1, 2, 4, 1, 3, 5, 1, 4, 2, 3, 6, 1, 5, 2, 4, 1, 2, 3, 7, 1, 6, 2, 5, 3, 4, 1, 2, 4, 8, 1, 7, 2, 6, 3, 5, 1, 2, 5, 1, 3, 4, 9, 1, 8, 2, 7, 3, 6, 4, 5, 1, 2, 6, 1, 3, 5, 2, 3, 4, 10, 1, 9, 2, 8, 3, 7, 4, 6, 1, 2, 7, 1, 3, 6, 1, 4, 5, 2, 3, 5, 1, 2, 3, 4, 11, 1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 1, 2, 8, 1, 3, 7, 1, 4, 6, 2, 3, 6, 2, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is the Abramowitz and Stegun ordering. - Franklin T. Adams-Watters, Apr 28 2006 LINKS Alois P. Heinz, Rows n = 1..32, flattened M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. EXAMPLE The partitions of 5 into distinct parts are [5], [1,4] and [2,3], so row 5 is 5,1,4,2,3. Triangle begins: [1]; [2]; [3], [1,2]; [4], [1,3]; [5], [1,4], [2,3]; [6], [1,5], [2,4], [1,2,3]; [7], [1,6], [2,5], [3,4], [1,2,4]; [8], [1,7], [2,6], [3,5], [1,2,5], [1,3,4]; [9], [1,8], [2,7], [3,6], [4,5], [1,2,6], [1,3,5], [2,3,4]; MAPLE b:= proc(n, i) b(n, i):= `if`(n=0, [[]], `if`(i>n, [],       [map(x->[i, x[]], b(n-i, i+1))[], b(n, i+1)[]]))     end: T:= n-> map(x-> x[], sort(b(n, 1)))[]: seq(T(n), n=1..12);  # Alois P. Heinz, Jun 22 2020 MATHEMATICA Array[SortBy[Map[Reverse, Select[IntegerPartitions[#], UnsameQ @@ # &]], Length] &, 12] // Flatten (* Michael De Vlieger, Jun 22 2020 *) b[n_, i_] := b[n, i] = If[n == 0, {{}}, If[i>n, {}, Join[Prepend[#, i]& /@ b[n-i, i+1], b[n, i+1]]]]; T[n_] := Sort[b[n, 1]]; Array[T, 12] // Flatten (* Jean-François Alcover, Jun 09 2021, after Alois P. Heinz *) CROSSREFS Cf. A118457, A118458 (partition lengths), A015723 (total row lengths), A036036, A000009, A246688. Sequence in context: A097293 A296656 A303945 * A344089 A329631 A239304 Adjacent sequences:  A026790 A026791 A026792 * A026794 A026795 A026796 KEYWORD nonn,tabf AUTHOR EXTENSIONS Incorrect program removed by Georg Fischer, Jun 22 2020 STATUS approved

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Last modified May 22 22:13 EDT 2022. Contains 353959 sequences. (Running on oeis4.)