A206438 Triangle read by rows which lists the squares of the parts of A135010.

1, 1, 4, 1, 1, 9, 1, 1, 1, 4, 4, 16, 1, 1, 1, 1, 1, 4, 9, 25, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 16, 9, 9, 36, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 9, 4, 25, 9, 16, 49, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 16, 4, 9, 9, 4, 36, 9, 25

Offset

1,3

Comments

Volumes of the parts in the section model of partitions version "boxes" in which each part of size k has a volume = k^2. Row sums of this triangle give A206440 and partial sums of A206440 give A066183.

Links

Alois P. Heinz, Rows n = 1..23, flattened

Formula

a(n) = A135010(n)^2.

Example

Written as a triangle:
1;
1,4;
1,1,9;
1,1,1,4,4,16;
1,1,1,1,1,4,9,25;
1,1,1,1,1,1,1,4,4,4,4,16,9,9,36;
1,1,1,1,1,1,1,1,1,1,1,4,4,9,4,25,9,16,49;

Mathematica

Table[Reverse@ConstantArray[{1}, PartitionsP[n - 1]] ~Join~ DeleteCases[Sort@PadRight[Reverse/@Cases[IntegerPartitions[n], x_ /; Last[x] != 1]], x_ /; x == 0, 2], {n, 1, 8}] ^2  // Flatten (* Robert Price, May 28 2020 *)

Crossrefs

Row n has length A138137(n).

Row sums give A206440.

Right border gives positives A000290.

Cf. A066183, A135010, A138121, A141285.

Sequence in context: A055107 A297193 A272867 * A331148 A128137 A232530

Adjacent sequences: A206435 A206436 A206437 * A206439 A206440 A206441

Keyword

nonn,tabf

Author

Omar E. Pol, Feb 08 2012

Status

approved