%I #11 Aug 08 2017 12:59:24

%S 1,0,-1,1,-1,-3,3,3,-6,2,10,-13,-9,29,-9,-43,55,32,-126,48,183,-243,

%T -121,541,-241,-765,1082,450,-2326,1171,3179,-4803,-1617,9993,-5601,

%U -13168,21250,5552,-42849,26489,54351,-93763,-17765,183347,-124086,-223422,412698,49827,-782881,576541,914279

%N A Chebyshev transform of the Padovan numbers.

%C A Chebyshev transform of the Padovan numbers A000931(n+3): if A(x) is the g.f. of a sequence, map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)).

%H G. C. Greubel, <a href="/A100049/b100049.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,-2,1,-2,0,-1).

%F G.f.: (1-x^2)*(1+x^2)^2/(1+2*x^2-x^3+2*x^4+x^6).

%F a(n) = -2*a(n-2) +a(n-3) -2*a(n-4) -a(n-6).

%F a(n) = n*Sum_{k=0..floor(n/2)} (-1)^k*binomial(n-k,k)*A000931(n-2*k+3)/(n-k).

%t LinearRecurrence[{0, -2, 1, -2, 0, -1}, {1, 0, -1, 1, -1, -3, 3}, 50] (* _G. C. Greubel_, Aug 08 2017 *)

%o (PARI) x='x+O('x^50); Vec((1-x^2)*(1+x^2)^2/(1+2*x^2-x^3+2*x^4+x^6)) \\ _G. C. Greubel_, Aug 08 2017

%Y Cf. A099443, A011655, A100047, A100048.

%K easy,sign

%O 0,6

%A _Paul Barry_, Oct 31 2004