Greek letters range from 0 to 3, Latin letters from 1 to 3. Subscripts in the Algol68 code are systematically one greater.
γgαβ:
jgαβ = 0
0g00 = 2t−3
jgkk = −2t−3
jgkn = 0 if k≠n

Γγαβ = ½ gγδ(∂αgβδ + ∂βgδα − ∂δgαβ)
This program computes several quantities for the space. It seems that that
Γγαβ = (−1/t)IF α=β⋀γ=0 ⋁ β=γ⋀α=0 ⋁ γ=α⋀β=0 THEN 1 ELSE 0 FI
which is a peculiar symmetry.
map:
mathAlgol 68
gαβg[α, β]
gαβgu[α, β]
αgβγdg[α, β, γ]
Γγαβchu[γ, α, β]
δΓγαβdchu(δ, γ, α, β)
Rαβγδrie[α, β, γ, δ]
Rαβγδriel[α, β, γ, δ]
Rαβrie2[α, β]
Rrie0
Cαβγδc[α, β, γ, δ]
Rμσαβ = − ∂βΓμσα + ∂αΓμσβ + ΓμραΓρσβ − ΓμρβΓρσα

Weyl Tensor = (too) = Cabcd = Rabcd
+ (gadRcb + gbcRad − gacRdb − gbdRca)/(4−2)
+ (gacgdb − gadgcb)R/((n−1)(n−2))

I am mystified that the Weyl tensor does not vanish—it is proportional to the Riemann tensor:

The program is less general that you might think at first glance. It assumes a diagonal metric when it inverts the matrix. (Here is a general matrix inversion routine.) It exploits the fact that gαβ and Γγαβ are each proportional to a power of t as it computes their derivative.

Rjk =
0000
0−2t−200
00−2t−20
000−2t−2
and thus this metric does not satisfy Einstein’s equations for any cosmological constant except with some matter density.

Square all this with decomposition!
More map:
mathAlgol 68
Sαβγδsu[α, β, γ, δ]
Sαβsu2[α, β]
Eαβγδe[α, β, γ, δ]
The two computations of the Weyl tensor agree!