cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

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%I A141577 #19 Sep 18 2024 10:31:49
%S A141577 -1,0,1,-1,-3,3,8,-9,-21,27,55,-80,-143,235,369,-685,-944,1983,2391,
%T A141577 -5705,-5985,16320,14769,-46441,-35803,131507,84824,-370665,-194813,
%U A141577 1040147,427767,-2906448,-874495,8088003,1564377,-22416669,-1971296,61883839,-1016657,-170165393,20507391,466069760
%N 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).
%D A141577 Martin Gardner, Mathematical Circus, Random House, New York, 1981, p. 165.
%H A141577 G. C. Greubel, <a href="/A141577/b141577.txt">Table of n, a(n) for n = 0..1000</a>
%H A141577 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,-3,3,-1).
%F A141577 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
%t A141577 LinearRecurrence[{1,-3,3,-1}, {-1,0,1,-1}, 51] (* _G. C. Greubel_, Sep 16 2024 *)
%o A141577 (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
%o A141577 (Magma)
%o A141577 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
%o A141577 (SageMath)
%o A141577 def A141577_list(prec):
%o A141577     P.<x> = PowerSeriesRing(ZZ, prec)
%o A141577     return P( (-1+x-2*x^2+x^3)/(1-x+3*x^2-3*x^3+x^4) ).list()
%o A141577 A141577_list(50) # _G. C. Greubel_, Sep 16 2024
%Y A141577 Cf. A141576.
%K A141577 sign,easy
%O A141577 0,5
%A A141577 Matt Wynne (mattwyn(AT)verizon.net), Aug 18 2008
%E A141577 Corrected and extended by _R. J. Mathar_, Aug 25 2008