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a(n) = a(n-1)^2 + 3 for n >=2 , where a(0) = 1, a(1) = 3.
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%I #8 May 29 2022 18:00:35

%S 1,3,12,147,21612,467078547,218162369067631212,

%T 47594819277201331861096436836588947,

%U 2265266822029455509816214491130485582138030749246532017266850242568812

%N a(n) = a(n-1)^2 + 3 for n >=2 , where a(0) = 1, a(1) = 3.

%C (a(n)) is a strong divisibility sequence.

%F a(n) = p(n,0), where p(n,x) is polynomial defined in A329433.

%t f[x_] := x^2 + 3; u[0, x_] := 1;

%t u[1, x_] := f[x]; u[n_, x_] := f[u[n - 1, x]]

%t Table [u[n, x] /. x -> 0, {n, 0, 10}]

%Y Cf. A329433.

%K nonn

%O 0,2

%A _Clark Kimberling_, Dec 31 2019