A354762 - OEIS

%I #10 Oct 01 2022 19:19:34

%S 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,

%T 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,

%U 6,28,28,1,28,1,1,28,3,28,3,1,28,3,1,1,28,6,28,6,1

%N Irregular triangle read by rows in which the row n lists the partition of n into the minimum number of triangular parts.

%C The representation of the partitions (for fixed n) is as (weakly) decreasing list of the parts.

%e The irregular triangle begins:

%e      0;

%e      1;

%e      1, 1;

%e      3;

%e      3, 1;

%e      3, 1, 1;

%e      6;

%e      6, 1;

%e      6, 1, 1;

%e      6, 3;

%e     10;

%e     10, 1;

%e     10, 1, 1;

%e     10, 3;

%e     10, 3, 1;

%e     15;

%e     15, 1;

%e     15, 1, 1;

%e     15, 3;

%e     15, 3, 1;

%e     15, 3, 1, 1;

%e     ...

%t Flatten[Join[{0}, Table[First[IntegerPartitions[n, All, Table[k(k+1)/2, {k, (Sqrt[1+8n]-1)/2}]]], {n, 35}]]]

%Y Cf. A000041, A000217, A007294.

%Y Cf. A001477 (row sums), A057944 (1st column), A057945 (row lengths).

%Y Cf. A354763.

%K nonn,easy,tabf

%O 0,5

%A _Stefano Spezia_, Jun 06 2022