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 A181864 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). 10
 1, 2, 7, 207, 700207, 207000000700207, 70020700000000000000207000000700207, 2070000007002070000000000000000000000000000000000070020700000000000000207000000700207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. For similarly defined sequences see A181754 through A181756 and A181865 through LINKS FORMULA 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 and where Pell(n) = A000129(n). RELATION WITH OTHER SEQUENCES a(n) has A113225(n-2) digits. a(n)^2 has Pell(n-1) digits. MAPLE 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); CROSSREFS Sequence in context: A247028 A333740 A306951 * A096463 A048560 A261267 Adjacent sequences:  A181861 A181862 A181863 * A181865 A181866 A181867 KEYWORD nonn,easy AUTHOR Peter Bala, Nov 28 2010 STATUS approved

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)