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

%I A239512 #8 Dec 13 2015 01:13:50
%S A239512 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,
%T A239512 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,
%U A239512 1,1,1,1,1,7,4,3,4,2,1,4,1,1,1,3,3,1
%N A239512 Irregular triangular array read by rows:  row n gives a list of the partitions of the Lucas numbers.
%C A239512 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.
%H A239512 Clark Kimberling, <a href="/A239512/b239512.txt">Table of n, a(n) for n = 1..1000</a>
%e A239512 The first 7 rows:
%e A239512 1
%e A239512 1 1
%e A239512 3 1 1 1
%e A239512 4 3 1 1 1 1 1
%e A239512 4 1 3 1 1 1 1 1 1 1
%e A239512 4 1 1 3 3 3 1 1 1 1 1 1 1 1 1
%e A239512 7 4 3 4 1 1 1 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1
%e A239512 The first 7 rows represent these partitions:
%e A239512 1
%e A239512 11
%e A239512 3, 111
%e A239512 4, 31, 1111
%e A239512 41, 311, 11111
%e A239512 411, 33, 3111, 111111
%e A239512 7, 43, 431, 41111, 3311, 311111, 1111111
%t A239512 LucasQ[n_] := IntegerQ[Sqrt[5 n^2 + 20]] || IntegerQ[Sqrt[5 n^2 - 20]];
%t A239512 Attributes[LucasQ] = {Listable}; TableForm[t = Map[Select[IntegerPartitions[#], And @@ LucasQ[#] &] &, Range[0, 12]]]  (* A239512, partitions *)
%t A239512 Flatten[t] (* A067592 *)
%t A239512 (* _Peter J. C. Moses_, Mar 24 2014 *)
%Y A239512 Cf. A239001, A000032, A067592.
%K A239512 nonn,tabf,easy
%O A239512 1,2
%A A239512 _Clark Kimberling_, Mar 25 2014