OFFSET
0,1
COMMENTS
Also known as unitary triangular hexagram numbers, according to the author.
After a(0), the sum of inner and outer perimeters of triangle edges forming each hexagram is [36n - 6], always 12 less than the number of triangles framing the hexagram. Where a(0)=12, the perimeter is also 12.
Compare with A270545, the number of equilateral triangle units forming perimeters of equilateral triangle, which follows the same application.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Peter M. Chema, Illustration of a(2)=78
Peter M. Chema, Illustration of initial terms [0 through 5]
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(0) = 12; thereafter, a(n) = 36*n + 6.
a(n) = 2*a(n-1)-a(n-2) for n>2. - Colin Barker, Mar 22 2016
G.f.: 6*(1+x)*(2+x) / (1-x)^2. - Colin Barker, Mar 22 2016
EXAMPLE
Illustration of initial terms are found in the three above links.
MATHEMATICA
CoefficientList[Series[6 (1 + x) (2 + x)/(1 - x)^2, {x, 0, 40}], x] (* Michael De Vlieger, Mar 23 2016 *)
Join[{12}, 36*Range[50]+6] (* or *) LinearRecurrence[{2, -1}, {12, 42, 78}, 50] (* Harvey P. Dale, Nov 03 2016 *)
PROG
(PARI) a(n) = if (!n, 12, 36*n + 6); \\ Michel Marcus, Mar 22 2016
(PARI) Vec(6*(1+x)*(2+x)/(1-x)^2 + O(x^50)) \\ Colin Barker, Mar 22 2016
(Magma) [12] cat [36*n + 6: n in [1..50]]; // Vincenzo Librandi, Mar 28 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter M. Chema, Mar 21 2016
EXTENSIONS
More terms from Vincenzo Librandi, Mar 28 2016
STATUS
approved