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a(n) is the number of edges of the polycube called "tower" described in A221529 where n is the longest side of its base.
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%I #34 Jun 08 2022 10:17:24

%S 12,12,27,36,51,72,84,105,117,144,165

%N a(n) is the number of edges of the polycube called "tower" described in A221529 where n is the longest side of its base.

%C The tower is a geometric object associated to all partitions of n.

%C The height of the tower equals A000041(n-1).

%F a(n) = A346530(n) + A346532(n) - 2 (Euler's formula).

%e For n = 1 the tower is a cube, and a cube has 12 edges, so a(1) = 12.

%Y Cf. A000203 (area of the terraces), A000041 (height of the terraces), A066186 (volume), A345023 (surface area), A346530 (number of faces), A346532 (number of vertices).

%Y Cf. A325301 (analog for the pyramid described in A245092).

%Y Cf. A221529, A236104, A237270, A237271, A237593, A336811, A338156, A340035, A340584.

%K nonn,more

%O 1,1

%A _Omar E. Pol_, Jul 22 2021