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A181864
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a(1) = 1, a(2) = 2. For n >= 3, a(n) is found by concatenating the squares of the first n-1 terms of the sequence and then dividing the resulting number by a(n-1).
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10
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OFFSET
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1,2
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COMMENTS
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The calculations for the first few values of the sequence are
... 2^2 = 4 so a(3) = 14/2 = 7
... 7^2 = 49 so a(4) = 1449/7 = 207
... 207^2 = 42849 so a(5) = 144942849/207 = 700207.
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LINKS
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FORMULA
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DEFINITION
a(1) = 1, a(2) = 2, and for n >= 3
(1)... a(n) = concatenate(a(1)^2,a(2)^2,...,a(n-1)^2)/a(n-1).
RECURRENCE RELATION
For n >= 2
(2)...a(n+2) = a(n+1) + 10^F(n,2)*a(n) = a(n+1) + 10^Pell(n)*a(n),
where F(n,2) is the Fibonacci polynomial F(n,x) evaluated at x = 2
RELATION WITH OTHER SEQUENCES
a(n)^2 has Pell(n-1) digits.
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MAPLE
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M:=8: a:=array(1..M):s:=array(1..M):
a[1]:=1:a[2]:=2:
s[1]:=convert(a[1]^2, string):
s[2]:=cat(s[1], convert(a[2]^2, string)):
for n from 3 to M do
a[n] := parse(s[n-1])/a[n-1];
s[n]:= cat(s[n-1], convert(a[n]^2, string));
end do:
seq(a[n], n = 1..M);
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CROSSREFS
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A000129, A113225, A181754, A181755, A181756, A181865, A181866,A181867, A181868, A181869, A181870
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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