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%I #14 Jul 31 2015 21:27:17
%S 0,0,0,1,3,5,5,0,-13,-34,-55,-55,0,144,377,610,610,0,-1597,-4181,
%T -6765,-6765,0,17711,46368,75025,75025,0,-196418,-514229,-832040,
%U -832040,0,2178309,5702887,9227465,9227465,0,-24157817,-63245986,-102334155,-102334155
%N a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4), a(0)=a(1)=a(2)=0, a(3)=1, a(4)=3.
%C Obeys also the recurrence a(n)=5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5), so the sequence is identical to its fifth differences (cf. A135356). a(n) = A138110(0,n): if A138110 is interpreted as an array with five rows, this is the top row.
%C The first differences are represented by A100334(n-1).
%C The 2nd differences are represented by A103311(n).
%C The 3rd differences are essentially represented by -A138003(n-2).
%C The 4th differences are represented by -A105371(n).
%C A102312 contains the absolute values of the terms which occur in pairs, for example a(5)=a(6)=5=A102312(1), a(10)=a(11)= -55 = -A102312(2).
%C Inverse BINOMIAL transform yields two zeros followed by A105384. - _R. J. Mathar_, Jul 04 2008
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, -4, 2, -1).
%F O.g.f.: x^3/(1-3x+4x^2-2x^3+x^4). - _R. J. Mathar_, Jul 04 2008
%t CoefficientList[Series[x^3/(1-3x+4x^2-2x^3+x^4),{x,0,45}],x] (* or *) LinearRecurrence[{3,-4,2,-1},{0,0,0,1},45] (* _Harvey P. Dale_, Jun 22 2011 *)
%Y Cf. A138003, A103311, A105371.
%K sign
%O 0,5
%A _Paul Curtz_, May 04 2008
%E Edited and extended by _R. J. Mathar_, Jul 04 2008
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