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A138003 Binomial transform of 1, 1, 0, -1, -1 (periodically continued).

%I A138003 #16 Dec 05 2023 09:22:32
%S A138003 1,2,3,3,0,-8,-21,-34,-34,0,89,233,377,377,0,-987,-2584,-4181,-4181,0,
%T A138003 10946,28657,46368,46368,0,-121393,-317811,-514229,-514229,0,1346269,
%U A138003 3524578,5702887,5702887,0,-14930352,-39088169,-63245986,-63245986
%N A138003 Binomial transform of 1, 1, 0, -1, -1 (periodically continued).
%C A138003 Shares many elements with A103311, as already indicated by the similarity of the two generating functions. First differences are essentially in A105371. - _R. J. Mathar_, May 02 2008
%C A138003 The longer of the two recurrences ensures that the sequence (like A133476) equals its 5th differences. - _R. J. Mathar_, May 02 2008
%H A138003 Paolo Xausa, <a href="/A138003/b138003.txt">Table of n, a(n) for n = 0..1000</a>
%H A138003 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,2,-1).
%F A138003 From _R. J. Mathar_, May 02 2008: (Start)
%F A138003 O.g.f.: (x^2-x+1)/(x^4-2*x^3+4*x^2-3*x+1).
%F A138003 a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5).
%F A138003 a(n) = 3a(n-1)-4a(n-2)+2a(n-3)-a(n-4). (End)
%t A138003 LinearRecurrence[{3,-4,2,-1},{1,2,3,3},50] (* _Paolo Xausa_, Dec 05 2023 *)
%o A138003 (PARI) a=[1,2,3,3];for(i=1,99,a=concat(a,3*a[#a]-4*a[#a-1]+2*a[#a-2]-a[#a-3]));a \\ _Charles R Greathouse IV_, Jun 02 2011
%Y A138003 Cf. A129929.
%K A138003 sign,easy
%O A138003 0,2
%A A138003 _Paul Curtz_, May 01 2008
%E A138003 Edited by _R. J. Mathar_, May 02 2008