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A138003 Binomial transform of 1, 1, 0, -1, -1 (periodically continued). 3

%I

%S 1,2,3,3,0,-8,-21,-34,-34,0,89,233,377,377,0,-987,-2584,-4181,-4181,0,

%T 10946,28657,46368,46368,0,-121393,-317811,-514229,-514229,0,1346269,

%U 3524578,5702887,5702887,0,-14930352,-39088169,-63245986,-63245986

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

%C 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 The longer of the two recurrences ensures that the sequence (like A133476) equals its 5th differences. - _R. J. Mathar_, May 02 2008

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,2,-1).

%F O.g.f.:(x^2-x+1)/(x^4-2*x^3+4*x^2-3*x+1). a(n)=5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5). a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4). - _R. J. Mathar_, May 02 2008

%o (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 Cf. A129929.

%K sign,easy

%O 0,2

%A _Paul Curtz_, May 01 2008

%E Edited by _R. J. Mathar_, May 02 2008

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)