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