A152035 Expansion of g.f. (1-2*x^2)/(1-2*x-2*x^2).

1, 2, 4, 12, 32, 88, 240, 656, 1792, 4896, 13376, 36544, 99840, 272768, 745216, 2035968, 5562368, 15196672, 41518080, 113429504, 309895168, 846649344, 2313089024, 6319476736, 17265131520, 47169216512, 128868696064, 352075825152, 961889042432, 2627929735168, 7179637555200, 19615134580736

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

Cf. A028860. Row sums of A322942.

Sequence in context: A181329 A293007 A028860 * A026151 A025178 A231295

Adjacent sequences: A152032 A152033 A152034 * A152036 A152037 A152038

Keyword

nonn,easy

Author

Roger L. Bagula, Nov 20 2008

Extensions

Edited by N. J. A. Sloane, Apr 11 2009, based on comments from Philippe Deléham and R. J. Mathar

More terms from Philippe Deléham, Sep 21 2009

Status

approved