Search: id:A002266
Results 1-1 of 1 results found.

%I A002266
%S A002266 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,
%T A002266 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,
%U A002266 12,12,12,12,13,13,13,13,13,14,14,14,14,14,15,15,15,15,15,16,16,16
%N A002266 Integers repeated 5 times.
%C A002266 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 (benoit7848c(AT)orange.fr), Jan 08 2006
%C A002266 Complement of A010874, since A010874(n)+5*a(n)=n. - Hieronymus Fischer 
               (Hieronymus.Fischer(AT)gmx.de), Jun 01 2007
%H A002266 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A002266 Floor(n/5), n>=0.
%F A002266 G.f.: x^5/((1-x)(1-x^5)).
%F A002266 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 (ppl(AT)spl.at), 
               May 15 2007
%F A002266 a(n)=(n-A010874(n))/5. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               May 29 2007
%F A002266 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 (azarian(AT)evansville.edu), Nov 08 2007
%F A002266 This sequence is also the sequence Floor(n*e^(-(1+sqrt(5))/2))(n>=1). 
               - Mohammad K. Azarian (azarian(AT)evansville.edu), May 13 2008
%Y A002266 Cf. A008648.
%Y A002266 a(n)=A010766(n, 5).
%Y A002266 Cf. A004526, A002264, A002265, A010761, A010762, A110532, A110533.
%Y A002266 Partial sums: A130520. Other related sequences: A004526, A010872, A010873, 
               A010874.
%Y A002266 Sequence in context: A104355 A092278 A105512 this_sequence A075249 A008648 
               A154099
%Y A002266 Adjacent sequences: A002263 A002264 A002265 this_sequence A002267 A002268 
               A002269
%K A002266 nonn,easy
%O A002266 0,11
%A A002266 N. J. A. Sloane (njas(AT)research.att.com).

Search completed in 0.002 seconds