A107300 a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) with a(0)=3, a(1)=2, a(3)=8.

3, 2, 8, 14, 40, 92, 236, 576, 1440, 3560, 8848, 21936, 54448, 135072, 335168, 831584, 2063360, 5119552, 12702656, 31517696, 78201600, 194033280, 481434368, 1194532096, 2963866368, 7353928192

Offset: 0

Author

Roger L. Bagula, May 20 2005

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,2,-2).

Crossrefs

Cf. A077937.

Programs

Magma

I:=[3,2,8]; [n le 3 select I[n] else 2*(Self(n-1) +Self(n-2) -Self(n-3)): n in [1..46]]; // G. C. Greubel, May 02 2022

Mathematica

LinearRecurrence[{2,2,-2}, {3,2,8}, 46]

SageMath

def A107300_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (3-4*x-2*x^2)/(1-2*x-2*x^2+2*x^3) ).list()
A107300_list(45) # G. C. Greubel, May 02 2022

Formula

G.f.: (3-4*x-2*x^2)/(1-2*x-2*x^2+2*x^3). [Sep 28 2009]

a(n) = 3*A077937(n) - 4*A077937(n-1) - 2*A077937(n-2). [Sep 28 2009]

a(n) = 2*(b1^n + b2^n + b3^n)/(b1 + b2 + b3), where b1, b2, and b3 and the roots of x^3 = 2*x^2 + 2*x - 2.

Extensions

Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009