A239512 Irregular triangular array read by rows: row n gives a list of the partitions of the Lucas numbers.

1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 3, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 4, 1, 3, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 4, 1, 1, 3, 3, 3, 2, 1, 3, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 4, 3, 4, 2, 1, 4, 1, 1, 1, 3, 3, 1

Offset

1,2

Comments

The number of partitions represented in row n is A067592(n). The parts of each partition are arranged in nonincreasing order, and the partitions are arranged in Mathematica order (reverse-lexicographic). The parts are the terms of the Lucas sequence, A000032(n), n >= 1.

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

The first 7 rows:
1
1 1
3 1 1 1
4 3 1 1 1 1 1
4 1 3 1 1 1 1 1 1 1
4 1 1 3 3 3 1 1 1 1 1 1 1 1 1
7 4 3 4 1 1 1 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1
The first 7 rows represent these partitions:
1
11
3, 111
4, 31, 1111
41, 311, 11111
411, 33, 3111, 111111
7, 43, 431, 41111, 3311, 311111, 1111111

Mathematica

LucasQ[n_] := IntegerQ[Sqrt[5 n^2 + 20]] || IntegerQ[Sqrt[5 n^2 - 20]];
Attributes[LucasQ] = {Listable}; TableForm[t = Map[Select[IntegerPartitions[#], And @@ LucasQ[#] &] &, Range[0, 12]]]  (* A239512, partitions *)
Flatten[t] (* A067592 *)
(* Peter J. C. Moses, Mar 24 2014 *)

Crossrefs

Cf. A239001, A000032, A067592.

Sequence in context: A334301 A139100 A237982 * A334439 A036037 A181317

Adjacent sequences: A239509 A239510 A239511 * A239513 A239514 A239515

Keyword

nonn,tabf,easy

Author

Clark Kimberling, Mar 25 2014

Status

approved