A354762 Irregular triangle read by rows in which the row n lists the partition of n into the minimum number of triangular parts.
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
Examples
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;
...
Crossrefs
Programs
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Mathematica
Flatten[Join[{0}, Table[First[IntegerPartitions[n, All, Table[k(k+1)/2, {k, (Sqrt[1+8n]-1)/2}]]], {n, 35}]]]
Comments