A370869 a(0) = 0; thereafter, a(n) = a(n-1)^2 - 3*A058891(n).

0, -3, 3, -15, -159, -73023, -1110092415, -26437810940723795199, 188534296956047109666345322462443132417, -138142952727263338693771981084959537243558105718529460985143718744222698198015

Offset

0,2

Comments

Numerators in the iteration f(0) = 0 and f(n) = f(n-1)^2 - 3/2. First values are 0, -3/2, 3/4, -15/16, -159/256, ... Denominators are A001146(n). We still don't know the behavior of this iteration (see links).

Links

Table of n, a(n) for n=0..9.

Jordana Cepelewicz, ‘Entropy Bagels’ and Other Complex Structures Emerge From Simple Rules, Quanta Magazine, 27 February 2024.

Holly Krieger and Brady Haran, The Mystery of Hyperbolicity, Numberphile video (2024).

Formula

a(n) = a(n-1)^2 - 3*A058891(n).

Mathematica

a[0]=0; a[n_]:=a[n]=a[n-1]^2-3*2^(2^(n-1)- 1); Array[a, 9, 0]

Crossrefs

Cf. A058891, A001146.

Sequence in context: A111674 A222505 A292356 * A209020 A258204 A258017

Adjacent sequences: A370866 A370867 A370868 * A370870 A370871 A370872

Keyword

sign

Author

Giorgos Kalogeropoulos, Mar 03 2024

Status

approved