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A002266
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Integers repeated 5 times.
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35
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0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16
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OFFSET
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0,11
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COMMENTS
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For n>3, number of consecutive "11's" after the (n+3) "1's" in the continued fraction for sqrt(L(n+2)/L(n)) where L(n) is the n-th Lucas number A000002 (see example). E.g. the continued fraction for sqrt(L(11)/L(9)) is [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 11, 58, 2, 4, 1, ....] with 12 consecutive ones followed by floor(11/5)=2 elevens. - Benoit Cloitre, Jan 08 2006
Complement of A010874, since A010874(n)+5*a(n)=n. - Hieronymus Fischer, Jun 01 2007
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LINKS
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Table of n, a(n) for n=0..82.
Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
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FORMULA
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Floor(n/5), n>=0.
G.f.: x^5/((1-x)(1-x^5)).
a(n)= -1 + Sum_{k=0..n} {[8*(sin(2*Pi*k/5))^2-5]^2-5}/20, with n>=0. a(n)= -1 + Sum_{k=0..n} 1/50*{-9*[k mod 5]+[(n+1) mod 5]+[(n+2) mod 5]+[(n+3) mod 5]+11*[(n+4) mod 5]}, with n>=0. - Paolo P. Lava, May 15 2007
a(n)=(n-A010874(n))/5. - Hieronymus Fischer, May 29 2007
Also, floor((n^5-1)/5*n^4) will produce this sequence. Moreover, floor((n^5-n^4)/(5*n^4-4*n^3)) (n>=1) will produce this sequence as well. - Mohammad K. Azarian, Nov 08 2007
This sequence is also the sequence Floor(n*e^(-(1+sqrt(5))/2))(n>=1). - Mohammad K. Azarian, May 13 2008
For n>=5, a(n)=floor(log_5(5^a(n-1)+5^a(n-2)+5^a(n-3)+5^a(n-4)+5^a(n-5))) [From Vladimir Shevelev, Jun 22 2010]
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PROG
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(Sage) [floor(n/5) - 1 for n in xrange(5, 88)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2009]
(Haskell)
a002266 = (`div` 5)
a002266_list = [0, 0, 0, 0, 0] ++ map (+ 1) a002266_list
-- Reinhard Zumkeller, Nov 27 2012
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CROSSREFS
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Cf. A008648.
a(n)=A010766(n, 5).
Cf. A004526, A002264, A002265, A010761, A010762, A110532, A110533.
Partial sums: A130520. Other related sequences: A004526, A010872, A010873, A010874.
Sequence in context: A104355 A092278 A105512 * A075249 A008648 A154099
Adjacent sequences: A002263 A002264 A002265 * A002267 A002268 A002269
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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