OFFSET
1,4
COMMENTS
In order to construct this sequence we use the following rules: T(1,1) = 1. For n >= 2, row n lists the last 2^(n-2) compositions from the n-th row of triangle A228351 and then the last 2^(n-2) compositions from the n-th row of triangle A228525. In both cases these compositions are listed in the same order as they are listed in the mentioned triangles.
Row n has length A001792(n-1).
Row sums give A001787, n >= 1.
First differs from A227736 at a(18).
EXAMPLE
Illustration of initial terms:
---------------------------------------
n j Diagram Composition j
---------------------------------------
. _
1 1 |_|_ 1;
2 1 |_| | 1, 1,
2 2 |_ _|_ 2;
3 1 |_ | | 2, 1,
3 2 |_|_| | 1, 1, 1,
3 3 |_| | 1, 2,
3 4 |_ _ _|_ 3;
4 1 |_ | | 3, 1,
4 2 |_|_ | | 1, 2, 1,
4 3 |_ | | | 2, 1, 1,
4 4 |_|_|_| | 1, 1, 1, 1,
4 5 |_| | | 1, 1, 2,
4 6 |_ _| | 2, 2,
4 7 |_| | 1, 3,
4 8 |_ _ _ _|_ 4;
5 1 |_ | | 4, 1,
5 2 |_|_ | | 1, 3, 1,
5 3 |_ | | | 2, 2, 1,
5 4 |_|_|_ | | 1, 1, 2, 1,
5 5 |_ | | | 3, 1, 1,
5 6 |_|_ | | | 1, 2, 1, 1,
5 7 |_ | | | | 2, 1, 1, 1,
5 8 |_|_|_|_| | 1, 1, 1, 1, 1,
5 9 |_| | | | 1, 1, 1, 2,
5 10 |_ _| | | 2, 1, 2,
5 11 |_| | | 1, 2, 2,
5 12 |_ _ _| | 3, 2,
5 13 |_| | | 1, 1, 3,
5 14 |_ _| | 2, 3,
5 15 |_| | 1, 4,
5 16 |_ _ _ _ _| 5;
.
Triangle begins:
[1];
[1,1], [2];
[2,1], [1,1,1], [1,2], [3];
[3,1], [1,2,1], [2,1,1], [1,1,1,1], [1,1,2], [2,2], [1,3], [4];
[4,1], [1,3,1], [2,2,1], [1,1,2,1], [3,1,1], [1,2,1,1], [2,1,1,1], [1,1,1,1,1], [1,1,1,2], [2,1,2], [1,2,2], [3,2], [1,1,3], [2,3], [1,4], [5];
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Sep 07 2013
STATUS
approved