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a(0)=4, a(n)=a(n-1)^2 - n for n > 0.
a=2; lst={}; Do[a=a^2-n; AppendTo[lst, a], {n, 0, 10}]; lst
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a(-10)=2, 4, a(n)=a(n-1)^2-n for n > 0.
Cf. A153059.
Definition amended by Georg Fischer, Jul 15 2022
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a(n) ~ c^(2^n), where c = 3.8643187364012066048723545708047003493006832597186603613771125549936188672... . - Vaclav Kotesovec, Dec 18 2014
RecurrenceTable[{a[0]==4, a[n]==a[n-1]^2-n}, a, {n, 0, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)
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