cp's OEIS Frontend

A176207 Permutations of partitions listed in A080577 with partition lengths listed in A176208; the table has shape A058884.

%I A176207 #9 Apr 22 2023 00:23:46
%S A176207 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,
%T A176207 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,
%U A176207 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
%N A176207 Permutations of partitions listed in A080577 with partition lengths listed in A176208; the table has shape A058884.
%C A176207 The permutations are selected by considering partial sums of A080577:
%C A176207   1
%C A176207   1 2 11
%C A176207   1 2 11 3 21 111
%C A176207   ...
%C A176207 then prepending values from A176206 yielding
%C A176207   1
%C A176207   2 11
%C A176207   3 21 12 111
%C A176207   4 31 22 211 13 121 1111
%C A176207   ...
%C A176207 Cases appearing in A080577 are excluded from {a(n)}.
%H A176207 Andrew Howroyd, <a href="/A176207/b176207.txt">Table of n, a(n) for n = 3..1607</a> (rows 3..12)
%e A176207 Triangle begins:
%e A176207   {{1,2}},
%e A176207   {{1,3}, {1,2,1}},
%e A176207   {{2,3}, {1 4}, {1,3,1}, {1,2,2}, {1,2,1,1}},
%e A176207 Or more concisely:
%e A176207   {12},
%e A176207   {13, 121},
%e A176207   {23, 14, 131, 122, 1211},
%e A176207   {24, 231, 15, 141, 132, 1311, 1221, 12111},
%e A176207   ...
%o A176207 (PARI) \\ here R(n) returns n-th row as vector of vectors.
%o A176207 L(n,k)={vecsort([Vecrev(p) | p<-partitions(k), p[#p] > n-k], , 4)}
%o A176207 R(n)={ concat(vector(n-1, k, [concat([n-k],p) | p<-L(n,k)])) }
%o A176207 { for(n=3, 6, print(concat(R(n)))) } \\ _Andrew Howroyd_, Apr 21 2023
%Y A176207 Cf. A058884, A080577, A176206, A176208.
%K A176207 nonn,tabf,uned
%O A176207 3,2
%A A176207 _Alford Arnold_, Apr 12 2010
%E A176207 Offset corrected and a(50) and beyond from _Andrew Howroyd_, Apr 21 2023