User blog comment:Vel!/Symbols function/@comment-5150073-20121219094119/@comment-5150073-20121220110122

I found that s(2n+6) >~ 3{n}3. So:

s(8) > 27

s(10) > 7625597484987

s(12) > 3^^3 (tritri)

s(14) > 3^^^^3 (g_1)