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A166105
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Quadratic recurrence from Sylvester's sequence, but starting with a(0)=1 and a(1)=2.
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3
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1, 2, 4, 14, 184, 33674, 1133904604, 1285739649838492214, 1653126447166808570252515315100129584, 2732827050322355127169206170438813672515557678636778921646668538491883474
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OFFSET
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0,2
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COMMENTS
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a(n) is the size of the set S(n) constructed recursively as follows: Let S(1) = {a,b} and let P(S) be the set of pairs (s,t) where s,t are members of S and s not equal to t. We define S(n+1) as the union of S(n) and P(S(n)). - David M. Cerna, Feb 07 2018
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LINKS
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FORMULA
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Sum_{n>=0} 1/a(n) = 1.82689305142092757947757234878575... (compare with Sum_{n>=0} 1/A000058(n) = 1).
a(n) ~ c^(2^n), where c = 1.385089248334672909882206535871311526236739234374149506334120193387331772... . - Vaclav Kotesovec, Jan 19 2015
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MAPLE
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a := proc(n) option remember: if n=0 then 1 elif n=1 then 2 elif n>=2 then procname(n-1)^2 - procname(n-2)^2 + procname(n-2) fi; end:
a:=1:A:=a : to 10 do a:=a*(a-1)+2 : A:=A, a od:
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MATHEMATICA
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RecurrenceTable[{a[n]==a[n-1]^2-a[n-2]^2+a[n-2], a[0]==1, a[1]==2}, a, {n, 0, 10}] (* Vaclav Kotesovec, Jan 19 2015 *)
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PROG
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(PARI) a(n)=if(n<2, [1, 2][n+1], a(n-1)^2-a(n-2)^2+a(n-2));
(GAP) a:= [1, 2];; for n in [3..13] do a[n]:= a[n-1]^2 - a[n-2]^2 + a[n-2]; od; a; # Muniru A Asiru, Feb 07 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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