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Number of partitions of Lucas(n).
1

%I #26 Sep 08 2022 08:46:16

%S 2,1,3,5,15,56,385,4565,124754,9289091,2552338241,3646072432125,

%T 42748078035954696,7274403582551733377346,

%U 37285884524590579748861394570,14531841772646818920248481411605550560,1400135408797883233268006240578157606704308520406

%N Number of partitions of Lucas(n).

%H Seiichi Manyama, <a href="/A272891/b272891.txt">Table of n, a(n) for n = 0..24</a>

%F a(n) = A000041(A000032(n)).

%e a(4) = A000041(A000032(4)) = 15 because there are fifteen partitions of Lucas(4) = 7, namely: {7}, {6,1}, {5,2}, {5,1,1}, {4,3}, {4,2,1}, {4,1,1,1}, {3,3,1}, {3,2,2}, {3,2,1,1}, {3,1,1,1,1}, {2,2,2,1}, {2,2,1,1,1}, {2,1,1,1,1,1}, {1,1,1,1,1,1,1}.

%t Table[PartitionsP[LucasL[n]], {n, 0, 18}]

%o (Magma) [NumberOfPartitions(Lucas(n)): n in [0..18]];

%Y Cf. A000032, A000041, A072214, A100845.

%K nonn

%O 0,1

%A _Vincenzo Librandi_, May 09 2016

%E Edited by _Bruno Berselli_, May 09 2016