Search: id:A100069
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%I A100069
%S A100069 1,4,18,76,326,1384,5892,25036,106438,452344,1922588,8170936,34726940,
%T A100069 147589264,627256088,2665837516,11329815878,48151714264,204644809932,
%U A100069 869740430056,3696396920116,15709686864304,66766169526008
%N A100069 Sum binomial(n,k)4^(n-2k), k=0..floor(n/2).
%C A100069 An inverse Chebyshev transform of x/(1-4x), where the Chebyshev transform 
               of g(x) is ((1-x^2)/(1+x^2))g(x/(1+x^2)) and the inverse transform 
               maps a g.f. A(x) to (1/sqrt(1-4x^2))A(xc(x^2)) where c(x) is the 
               g.f. of the Catalan numbers A000108. In general, sum{k=0..floor(n/
               2), binomial(n,k)r^(n-k)} has g.f. 2x/((sqrt(1-4x^2)(r*sqrt(1-4x^2)+r*x-r).
%F A100069 G.f.: x/((sqrt(1-4x^2)(2sqrt(1-4x^2)+2x-2); a(n)=sum{k=0..floor(n/2), 
               binomial(n, k)4^(n-2k)}; a(n)=sum{k=0..n, binomial(n, (n-k)/2)(1+(-1)^(n-k)4^k/
               2}.
%Y A100069 Cf. A027306, A100067, A100068.
%Y A100069 Sequence in context: A108012 A017958 A017959 this_sequence A058870 A112619 
               A037965
%Y A100069 Adjacent sequences: A100066 A100067 A100068 this_sequence A100070 A100071 
               A100072
%K A100069 easy,nonn
%O A100069 0,2
%A A100069 Paul Barry (pbarry(AT)wit.ie), Nov 02 2004

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