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%I #14 Mar 17 2017 11:02:18
%S 1,0,0,4,-4,20,-20,84,-84,340,-340,1364,-1364,5460,-5460,21844,-21844,
%T 87380,-87380,349524,-349524,1398100,-1398100,5592404,-5592404,
%U 22369620,-22369620,89478484,-89478484,357913940,-357913940,1431655764,-1431655764,5726623060
%N Expansion of (1+x-4*x^2) / ((1+x)*(1-4*x^2)).
%C Binomial transform is A046717 (with extra leading 1).
%H Colin Barker, <a href="/A087213/b087213.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,4,4).
%F a(2*n+1) = A002450(n) = A001045(2*n).
%F a(2*n+2) = -A002450(n) = -A001045(2*n).
%F a(n) = 2^n/6 - (-2)^n/2 + 4*(-1)^n/3.
%F a(n) = -a(n-1)+4*a(n-2)+4*a(n-3) for n>2.
%t CoefficientList[Series[(1 + x - 4 x^2)/((1 + x) (1 - 4 x^2)), {x, 0, 33}], x] (* or *) {1, 0}~Join~LinearRecurrence[{-1, 4, 4}, {0, 4, -4}, 32] (* _Michael De Vlieger_, Mar 17 2017 *)
%o (PARI) Vec((1 + x - 4*x^2) / ((1 + x)*(1 - 2*x)*(1 + 2*x)) + O(x^40)) \\ _Colin Barker_, Mar 17 2017
%K easy,sign
%O 0,4
%A _Paul Barry_, Aug 26 2003
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