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A356888
a(n) = ((n-1)^2 + 2)*2^(n-2).
0
1, 3, 12, 44, 144, 432, 1216, 3264, 8448, 21248, 52224, 125952, 299008, 700416, 1622016, 3719168, 8454144, 19070976, 42729472, 95158272, 210763776, 464519168, 1019215872, 2227175424, 4848615424, 10519314432, 22749904896, 49056579584, 105495134208, 226291089408
OFFSET
1,2
a(n) is the number of fixed polyiamonds of minimal area 2*n-1 that touch each side of a triangle formed in the triangular lattice. n designates the number of triangles that touch each side of the larger triangle.
FORMULA
G.f.: -x*(6*x^2-3*x+1)/(2*x-1)^3.
E.g.f.: (exp(2*x)*(3 - 2*x + 4*x^2) - 3)/4. - Stefano Spezia, Sep 02 2022
EXAMPLE
a(3) = 12. Up to rotations and reflections there are 3 possibilities.
* * *
/ \ / \ / \
/ \ / \ / \
*-----* *-----* *-----*
/ \ / \ / \ /#\ /#\ /#\
/ \ / \ / \ /###\ /###\ /###\
*-----*-----* *-----*-----* *-----*-----*
/#\###/#\###/#\ /#\###/#\###/ \ / \###/#\###/ \
/###\#/###\#/###\ /###\#/###\#/ \ / \#/###\#/ \
*-----*-----*-----* *-----*-----*-----* *-----*-----*-----*
CROSSREFS
Cf. A334551.
Sequence in context: A290918 A012873 A282082 * A167477 A190051 A220633
KEYWORD
nonn,easy
AUTHOR
Jack Hanke, Sep 02 2022
STATUS
approved

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Last modified September 20 01:57 EDT 2024. Contains 376015 sequences. (Running on oeis4.)