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A239512 Irregular triangular array read by rows:  row n gives a list of the partitions of the Lucas numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A026792 A139100 A237982 * A036037 A181317 A080577

Adjacent sequences:  A239509 A239510 A239511 * A239513 A239514 A239515

KEYWORD

nonn,tabf,easy

AUTHOR

Clark Kimberling, Mar 25 2014

STATUS

approved

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Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)