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A354762
Irregular triangle read by rows in which the row n lists the partition of n into the minimum number of triangular parts.
1
0, 1, 1, 1, 3, 3, 1, 3, 1, 1, 6, 6, 1, 6, 1, 1, 6, 3, 10, 10, 1, 10, 1, 1, 10, 3, 10, 3, 1, 15, 15, 1, 15, 1, 1, 15, 3, 15, 3, 1, 15, 3, 1, 1, 21, 21, 1, 21, 1, 1, 21, 3, 21, 3, 1, 21, 3, 1, 1, 21, 6, 28, 28, 1, 28, 1, 1, 28, 3, 28, 3, 1, 28, 3, 1, 1, 28, 6, 28, 6, 1
OFFSET
0,5
COMMENTS
The representation of the partitions (for fixed n) is as (weakly) decreasing list of the parts.
EXAMPLE
The irregular triangle begins:
0;
1;
1, 1;
3;
3, 1;
3, 1, 1;
6;
6, 1;
6, 1, 1;
6, 3;
10;
10, 1;
10, 1, 1;
10, 3;
10, 3, 1;
15;
15, 1;
15, 1, 1;
15, 3;
15, 3, 1;
15, 3, 1, 1;
...
MATHEMATICA
Flatten[Join[{0}, Table[First[IntegerPartitions[n, All, Table[k(k+1)/2, {k, (Sqrt[1+8n]-1)/2}]]], {n, 35}]]]
CROSSREFS
Cf. A001477 (row sums), A057944 (1st column), A057945 (row lengths).
Cf. A354763.
Sequence in context: A213657 A215596 A268676 * A180938 A123561 A323626
KEYWORD
nonn,easy,tabf
AUTHOR
Stefano Spezia, Jun 06 2022
STATUS
approved