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

Author

Clark Kimberling, Mar 25 2014

Keywords

• nonn
• tabf
• easy

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.

Examples

			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
		

Links

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

Crossrefs

Cf. A239001, A000032, A067592.

Programs

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 *)