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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).
2
-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
0,5
REFERENCES
Martin Gardner, Mathematical Circus, Random House, New York, 1981, p. 165.
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
MATHEMATICA
LinearRecurrence[{1, -3, 3, -1}, {-1, 0, 1, -1}, 51] (* G. C. Greubel, Sep 16 2024 *)
PROG
(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
(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
(SageMath)
def A141577_list(prec):
P.<x> = 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
CROSSREFS
Cf. A141576.
Sequence in context: A323654 A092481 A099508 * A245142 A123315 A237113
KEYWORD
sign,easy
AUTHOR
Matt Wynne (mattwyn(AT)verizon.net), Aug 18 2008
EXTENSIONS
Corrected and extended by R. J. Mathar, Aug 25 2008
STATUS
approved