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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
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
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
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Mar 25 2014
STATUS
approved