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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
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
KEYWORD
nonn,tabf
AUTHOR
EXTENSIONS
Incorrect program removed by Georg Fischer, Jun 22 2020
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)