OFFSET
0,2
COMMENTS
Essentially same as A028860. - Philippe Deléham, Sep 21 2009
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,2).
FORMULA
a(n) = 2*(a(n-1) + a(n-2)) for n >= 3. - Peter Luschny, Jan 03 2019
MAPLE
a := proc(n) option remember;
`if`(n < 3, [1, 2, 4][n+1], 2*(a(n-1) + a(n-2))) end:
seq(a(n), n=0..31); # Peter Luschny, Jan 03 2019
MATHEMATICA
f[n_] = 2^n*Product[(1 + 2*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}]; Table[FullSimplify[ExpandAll[f[n]]], {n, 0, 15}]
CoefficientList[Series[(1-2x^2)/(1-2x-2x^2), {x, 0, 40}], x] (* Harvey P. Dale, Sep 23 2014 *)
LinearRecurrence[{2, 2}, {1, 2, 4}, 40] (* Harvey P. Dale, May 12 2023 *)
PROG
(Magma) [1] cat [n le 2 select 2^n else 2*(Self(n-1) +Self(n-2)): n in [1..30]]; // G. C. Greubel, Sep 20 2023
(SageMath)
@CachedFunction
def a(n): # a = A152035
if n<3: return (1, 2, 4)[n]
else: return 2*(a(n-1) + a(n-2))
[a(n) for n in range(31)] # G. C. Greubel, Sep 20 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Nov 20 2008
EXTENSIONS
More terms from Philippe Deléham, Sep 21 2009
STATUS
approved