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A099495 A Chebyshev transform of Fib(n)^2. 0


%S 0,1,1,2,6,12,25,55,118,254,548,1179,2539,5470,11780,25370,54641,

%T 117681,253452,545866,1175642,2532005,5453235,11744748,25294914,

%U 54478198,117330859,252697979,544241040,1172143560,2524470640,5437006381

%N A Chebyshev transform of Fib(n)^2.

%C A Chebyshev transform of A007598, which has g.f. x(1-x)/((1+x)(1-3x+x^2)). The image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,3,-1,2,-1).

%F G.f.: x(1-x+x^2)/((1+x+x^2)(1-3x+3x^2-3x^3+x^4)); a(n)=2a(n-1)-a(n-2)+3a(n-3)-a(n-4)+2a(n-5)-a(n-6); a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*F(n-2k)^2}.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Oct 19 2004

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Last modified May 18 13:09 EDT 2021. Contains 343995 sequences. (Running on oeis4.)