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A generalized Chebyshev transform of the Jacobsthal numbers.
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%I #6 Jun 13 2015 00:51:47

%S 0,1,1,7,11,47,95,327,759,2343,5863,17095,44551,126023,335687,934343,

%T 2518215,6948807,18846663,51765703,140875207,385980871,1052314055,

%U 2879386055,7857807815,21485572551,58664391111,160344666567

%N A generalized Chebyshev transform of the Jacobsthal numbers.

%C Apply the Riordan array (1/(1-2x^2),x/(1-2x^2)) to A001045.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-2,-4).

%F G.f.: x/(1-x-6x^2+2x^3+4x^4); a(n)=sum{k=0..floor(n/2), 2^k*C(n-k, k)*A001045(n-2k)}; a(n)=sqrt(3)(sqrt(3)+1)^(n+1)/18+sqrt(3)(sqrt(3)-1)^(n+1)(-1)^n/18-2^(n+1)(-1)^n/9-1/9.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Apr 23 2005