cp's OEIS Frontend

A354762 Irregular triangle read by rows in which the row n lists the partition of n into the minimum number of triangular parts.

%I A354762 #10 Oct 01 2022 19:19:34
%S A354762 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 A354762 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 A354762 6,28,28,1,28,1,1,28,3,28,3,1,28,3,1,1,28,6,28,6,1
%N A354762 Irregular triangle read by rows in which the row n lists the partition of n into the minimum number of triangular parts.
%C A354762 The representation of the partitions (for fixed n) is as (weakly) decreasing list of the parts.
%e A354762 The irregular triangle begins:
%e A354762      0;
%e A354762      1;
%e A354762      1, 1;
%e A354762      3;
%e A354762      3, 1;
%e A354762      3, 1, 1;
%e A354762      6;
%e A354762      6, 1;
%e A354762      6, 1, 1;
%e A354762      6, 3;
%e A354762     10;
%e A354762     10, 1;
%e A354762     10, 1, 1;
%e A354762     10, 3;
%e A354762     10, 3, 1;
%e A354762     15;
%e A354762     15, 1;
%e A354762     15, 1, 1;
%e A354762     15, 3;
%e A354762     15, 3, 1;
%e A354762     15, 3, 1, 1;
%e A354762     ...
%t A354762 Flatten[Join[{0}, Table[First[IntegerPartitions[n, All, Table[k(k+1)/2, {k, (Sqrt[1+8n]-1)/2}]]], {n, 35}]]]
%Y A354762 Cf. A000041, A000217, A007294.
%Y A354762 Cf. A001477 (row sums), A057944 (1st column), A057945 (row lengths).
%Y A354762 Cf. A354763.
%K A354762 nonn,easy,tabf
%O A354762 0,5
%A A354762 _Stefano Spezia_, Jun 06 2022