A141577 a(0) = -1; a(1) = 0; a(2) = 1; a(3) = -1; a(n) = a(n-1) - 3*a(n-2) + 3*a(n-3) - a(n-4).

-1, 0, 1, -1, -3, 3, 8, -9, -21, 27, 55, -80, -143, 235, 369, -685, -944, 1983, 2391, -5705, -5985, 16320, 14769, -46441, -35803, 131507, 84824, -370665, -194813, 1040147, 427767, -2906448, -874495, 8088003, 1564377, -22416669, -1971296, 61883839, -1016657, -170165393, 20507391, 466069760

Offset: 0

Author

Matt Wynne (mattwyn(AT)verizon.net), Aug 18 2008

Keywords

• sign
• easy

References

• Martin Gardner, Mathematical Circus, Random House, New York, 1981, p. 165.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-3,3,-1).

Crossrefs

Cf. A141576.

Programs

Magma

I:=[-1,0,1,-1]; [n le 4 select I[n] else Self(n-1) -3*Self(n-2) +3*Self(n-3) -Self(n-4): n in [1..50]]; // G. C. Greubel, Sep 16 2024

Mathematica

LinearRecurrence[{1,-3,3,-1}, {-1,0,1,-1}, 51] (* G. C. Greubel, Sep 16 2024 *)

PARI

my(x='x+O('x^99)); Vec((1-x+2*x^2-x^3)/(-1+x-3*x^2+3*x^3-x^4)) \\ Altug Alkan, Dec 17 2017

SageMath

def A141577_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (-1+x-2*x^2+x^3)/(1-x+3*x^2-3*x^3+x^4) ).list()
A141577_list(50) # G. C. Greubel, Sep 16 2024

Formula

O.g.f.: (-1+x-2*x^2+x^3)/(1-x+3*x^2-3*x^3+x^4). - R. J. Mathar, Aug 25 2008

Extensions

Corrected and extended by R. J. Mathar, Aug 25 2008