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A176207
Permutations of partitions listed in A080577 with partition lengths listed in A176208; the table has shape A058884.
3
1, 2, 1, 3, 1, 2, 1, 2, 3, 1, 4, 1, 3, 1, 1, 2, 2, 1, 2, 1, 1, 2, 4, 2, 3, 1, 1, 5, 1, 4, 1, 1, 3, 2, 1, 3, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 3, 4, 2, 5, 2, 4, 1, 2, 3, 2, 2, 3, 1, 1, 1, 6, 1, 5, 1, 1, 4, 2, 1, 4, 1, 1, 1, 3, 3, 1, 3, 2, 1, 1, 3, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1
OFFSET
3,2
COMMENTS
The permutations are selected by considering partial sums of A080577:
1
1 2 11
1 2 11 3 21 111
...
then prepending values from A176206 yielding
1
2 11
3 21 12 111
4 31 22 211 13 121 1111
...
Cases appearing in A080577 are excluded from {a(n)}.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 3..1607 (rows 3..12)
EXAMPLE
Triangle begins:
{{1,2}},
{{1,3}, {1,2,1}},
{{2,3}, {1 4}, {1,3,1}, {1,2,2}, {1,2,1,1}},
Or more concisely:
{12},
{13, 121},
{23, 14, 131, 122, 1211},
{24, 231, 15, 141, 132, 1311, 1221, 12111},
...
PROG
(PARI) \\ here R(n) returns n-th row as vector of vectors.
L(n, k)={vecsort([Vecrev(p) | p<-partitions(k), p[#p] > n-k], , 4)}
R(n)={ concat(vector(n-1, k, [concat([n-k], p) | p<-L(n, k)])) }
{ for(n=3, 6, print(concat(R(n)))) } \\ Andrew Howroyd, Apr 21 2023
CROSSREFS
KEYWORD
nonn,tabf,uned
AUTHOR
Alford Arnold, Apr 12 2010
EXTENSIONS
Offset corrected and a(50) and beyond from Andrew Howroyd, Apr 21 2023
STATUS
approved