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%I #14 Jan 14 2024 11:48:44
%S 1,2,8,32,256,4096,65536,2097152,134217728,8589934592,1099511627776,
%T 281474976710656,72057594037927936,36893488147419103232,
%U 37778931862957161709568,38685626227668133590597632
%N Hankel transform of expansion of (1/(1-x^2))c(x/(1-x^2)), where c(x) is the g.f. of A000108.
%C Hankel transform of A105864.
%C The sequence 1,1,2,8,... with general term 2^floor(n^2/3) is the Hankel transform of A109033. - _Paul Barry_, Dec 14 2008
%F a(n) = 2^floor((n+1)^2/3);
%F a(n) = Product_{k=1..n} (5/3 - 2*cos(2*Pi*k/3)/3)^(n-k+1);
%F a(n) = Product_{k=1..n} A130196(k)^(n-k+1).
%F a(n) = 4*a(n-1)*a(n-3)/a(n-4). Somos-4 sequence associated to, e.g., y^2 = 1 - 8x + 16x^2 - 8x^3. - _Paul Barry_, Nov 27 2009
%F a(n) = a(-2-n) for all n in Z. - _Michael Somos_, May 12 2022
%t a[ n_] := 2^Quotient[(n+1)^2, 3]; (* _Michael Somos_, May 12 2022 *)
%o (PARI) {a(n) = 2^((n+1)^2\3)}; /* _Michael Somos_, May 12 2022 */
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 08 2007
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