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%I #26 Mar 22 2023 11:07:36
%S 1,5,265,37220045,103124220135120334842385,
%T 2193370648451279691104497113491599222165108730278225579497595691360405
%N a(0) = 1, a(n+1) = 2*a(n)^3 + 3*a(n).
%C a(6) has 209 digits and is too large to include.
%C Except for the first term, this is a subsequence of A175180.
%C The squares larger than 1 are in A076445.
%F a(n) = sqrt(2) * sinh( 3^n * arcsinh(1/sqrt(2)) ) = (1+sqrt(3))/2 * (2+sqrt(3))^((3^n-1)/2) + (1-sqrt(3))/2 * (2-sqrt(3))^((3^n-1)/2). - _Max Alekseyev_, Sep 04 2018
%t RecurrenceTable[{a[0] == 1, a[n] == 2*a[n - 1]^3 + 3*a[n - 1]}, a[n], {n, 5}]
%t NestList[2#^3+3#&,1,5] (* _Harvey P. Dale_, Mar 22 2023 *)
%o (PARI) a=1; print1(a, ", "); for(n=1, 5, b=2*a^3+3*a; print1(b, ", "); a=b);
%o (PARI) { A238799(n) = my(q=Mod(x,x^2-3)); lift( (1+q)*(2+q)^((3^n-1)/2) + (1-q)*(2-q)^((3^n-1)/2) )/2; } \\ _Max Alekseyev_, Sep 04 2018
%Y Cf. A175180.
%K nonn,easy
%O 0,2
%A _Arkadiusz Wesolowski_, Mar 05 2014
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