OFFSET
0,1
COMMENTS
a(n) is the curvature (rounded down) of circles inscribed between a unit circle and a circumscribed equilateral triangle. See illustration.
Apart from the first term the same as A168607. - R. J. Mathar, Jul 09 2015
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Kival Ngaokrajang, Illustration of initial terms
Index entries for linear recurrences with constant coefficients, signature (4,-3).
FORMULA
From Colin Barker, Jul 07 2015: (Start)
a(n) = 3^n + 2 for n>0.
a(n) = 4*a(n-1) - 3*a(n-2) for n>2.
G.f.: (3*x^2-11*x+4) / ((x-1)*(3*x-1)).
(End)
MATHEMATICA
Table[Floor[(3^n + 1)^2/3^n], {n, 0, 30}] (* Michael De Vlieger, Jul 07 2015 *)
PROG
(PARI)
a(n)=floor((3^n+1)^2/3^n)
for (n=0, 100, print1(a(n), ", "))
(PARI) Vec((3*x^2-11*x+4)/((x-1)*(3*x-1)) + O(x^100)) \\ Colin Barker, Jul 07 2015
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Kival Ngaokrajang, Jul 07 2015
STATUS
approved