The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A211988 The Berndt-type sequence number 9 for the argument 2*Pi/13. 11
 0, -6, -37, 676, 2882, 12502, -196209, -856850, -3740697, 58876883, 257003504, 1121852777, -17656510365, -77073076671, -336434457597, 5295048110651, 23113603862267, 100894018986142, -1587942800101489, -6931585922526870, -30257313674299627, 476211413709501353 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) + A218655(n)*sqrt(13)  = A(2*n+1)*13^((1+floor(n/3))/2)*sqrt(2*(13 + 3*sqrt(13))/13), where A(n) is defined below. The sequence A(n) from the name of a(n) is defined  by the relation A(n) = s(1)^(-n) + s(3)^(-n) + s(9)^(-n), where s(j) := 2*sin(2*Pi*j/13). The sequence with respective positive powers is discussed in A216508 (see sequence Y(n) in Comments to A216508). It follows that A(n) = sqrt((13-3*sqrt(13))/2)*A(n-1) + (sqrt(13)-3)*A(n-2)/2 - sqrt((13-3*sqrt(13))/26)*A(n-3), with A(-1) = sqrt((13-3*sqrt(13))/2), A(0)=3, and A(1) = sqrt((13-3*sqrt(13))/2). We note that s(1) + s(3) + s(9) = s(1)^(-1) + s(3)^(-1) + s(9)^(-1) = sqrt((13-3*sqrt(13))/2), sqrt(2*sqrt(13))*(s(1)^(-3) + s(3)^(-3) + s(9)^(-3)) = sqrt((97*sqrt(13)-339), and  s(1)^(-9) + s(3)^(-9) + s(9)^(-9) = (131/13)*sqrt(2834 - 786*sqrt(13)). The numbers of other Berndt-type sequences for the argument 2*Pi/13 in crossrefs are given. REFERENCES R. Witula and D. Slota, Quasi-Fibonacci numbers of order 13 on the occasion of the Thirteenth International Conference on Fibonacci Numbers and their Applications, Congressus Numerantium, 201 (2010), 89-107. R. Witula, On some applications of formulas for sums of the unimodular complex numbers, Wyd. Pracowni Komputerowej Jacka Skalmierskiego, Gliwice 2011 (in Polish). LINKS CROSSREFS Cf. A216605, A216486, A216508, A216597, A216540, A161905, A217548, A217549, A216450. Sequence in context: A041062 A240324 A283636 * A285934 A083373 A320988 Adjacent sequences:  A211985 A211986 A211987 * A211989 A211990 A211991 KEYWORD sign AUTHOR Roman Witula, Oct 25 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 24 12:01 EDT 2022. Contains 354033 sequences. (Running on oeis4.)