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a(n) is the number of triangular partitions of size n with just one removable cell.
1

%I #9 Jan 01 2024 13:31:03

%S 1,2,2,2,4,2,2,6,4,2,8,2,4,10,6,2,10,6,8,12,6,2,18,6,8,16,8,8,24,2,6,

%T 20,14,12,26,6,6,24,22,6,30,6,20,30,10,8,36,14,18,32,18,4,48,18,22,30,

%U 14,12,52,14,20,42,26,24,44,6,20,52,38,12,54,10,26

%N a(n) is the number of triangular partitions of size n with just one removable cell.

%H Sergi Elizalde and Alejandro B. Galván, <a href="https://arxiv.org/abs/2312.16353">Triangular partitions: enumeration, structure, and generation</a>, arXiv:2312.16353 [math.CO], (2023).

%F See the g.f. in Proposition 6.2. of Elizalde and Galván.

%Y The number of triangular partitions of size n with any number of removable cells is in A352882.

%Y Cf. A368554 (with two removable cells).

%K nonn

%O 1,2

%A _Alejandro B. Galván_, Dec 29 2023