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

Author

Roger L. Bagula, Nov 20 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A028860. Row sums of A322942.

Programs

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

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 *)

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

Formula

a(n) = 2*(a(n-1) + a(n-2)) for n >= 3. - Peter Luschny, Jan 03 2019

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