A238799 a(0) = 1, a(n+1) = 2*a(n)^3 + 3*a(n).

1, 5, 265, 37220045, 103124220135120334842385, 2193370648451279691104497113491599222165108730278225579497595691360405

Offset

0,2

Comments

a(6) has 209 digits and is too large to include.

Except for the first term, this is a subsequence of A175180.

The squares larger than 1 are in A076445.

Links

Table of n, a(n) for n=0..5.

Formula

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

Mathematica

RecurrenceTable[{a[0] == 1, a[n] == 2*a[n - 1]^3 + 3*a[n - 1]}, a[n], {n, 5}]
NestList[2#^3+3#&, 1, 5] (* Harvey P. Dale, Mar 22 2023 *)

Prog

(PARI) a=1; print1(a, ", "); for(n=1, 5, b=2*a^3+3*a; print1(b, ", "); a=b);
(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

Crossrefs

Cf. A175180.

Sequence in context: A086656 A034602 A175180 * A113257 A180820 A140001

Adjacent sequences: A238796 A238797 A238798 * A238800 A238801 A238802

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Mar 05 2014

Status

approved