OFFSET
1,1
COMMENTS
FORMULA
DEFINITION
a(1) = 2, a(2) = 1, and for n >= 3
(1)... a(n) = concatenate (a(n-1)^2,a(n-2)^2,...,a(1)^2)/a(n-1).
RECURRENCE RELATION
For n >= 2,
(2)... a(n+2) = 10^F(n,2)*a(n+1) + a(n) = 10^Pell(n)*a(n+1) + a(n),
where F(n,2) is the n-th Fibonacci polynomial F(n,x) evaluated at
x = 2, and Pell(n) = A000129(n).
a(n) has A024537(n-2) digits.
MAPLE
M:=7:
a:=array(1..M):s:=array(1..M):
a[1]:=2:a[2]:=1:
s[1]:=convert(a[1]^2, string):
s[2]:=cat(convert(a[2]^2, string), s[1]):
for n from 3 to M do
a[n] := parse(s[n-1])/a[n-1];
s[n]:= cat(convert(a[n]^2, string), s[n-1]);
end do:
seq(a[n], n = 1..M);
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Peter Bala, Nov 29 2010
STATUS
approved