OFFSET
1,2
COMMENTS
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.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (6,-12,8).
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.
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MATHEMATICA
LinearRecurrence[{6, -12, 8}, {1, 3, 12}, 30] (* Paolo Xausa, Oct 07 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jack Hanke, Sep 02 2022
STATUS
approved