OFFSET
1,2
COMMENTS
The small stellated dodecahedron is a 3D nonconvex regular polyhedron represented by the Schlaefli symbol {5/2, 5}.
When truncated, a degenerate dodecahedron is produced. It is then easy to recognize that every small stellated dodecahedron can be constructed by morphing the 12 pentagonal faces of a regular dodecahedron into pentagonal pyramids.
The last digits form a cycle of length 20 [1, 2, 6, 6, ..., 1, 2, 6, 6].
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Wikipedia, Small stellated dodecahedron
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) == a(n+20) (mod 10).
From Colin Barker, Aug 20 2018: (Start)
G.f.: x*(1 + 28*x + 34*x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
MATHEMATICA
Table[(n (14 - 33 n + 21 n^2)) / 2, {n, 45}] (* Vincenzo Librandi, Aug 27 2018 *)
CoefficientList[Series[(1 + 28*x + 34*x^2) / (1 - x)^4 , {x, 0, 45}], x] (* or *)
LinearRecurrence[{4, -6, 4, -1}, {1, 32, 156, 436}, 45] (* Stefano Spezia, Sep 02 2018 *)
PROG
(PARI) Vec(x*(1 + 28*x + 34*x^2) / (1 - x)^4 + O(x^40)) \\ Colin Barker, Aug 20 2018
(PARI) a(n) = (n*(14 - 33*n + 21*n^2)) / 2 \\ Colin Barker, Aug 20 2018
(Magma) [n*(21*n^2-33*n+14)/2: n in [1..40]]; // Vincenzo Librandi, Aug 27 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alejandro J. Becerra Jr., Aug 19 2018
EXTENSIONS
More terms from Colin Barker, Aug 20 2018
STATUS
approved