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A217548 The Berndt-type sequences number 7 for the argument 2*Pi/13. 5
6, 7, -65, -295, -1303, 20631, 89967, 392616, -6178549, -26970688, -117731275, 1852943703, 8088348131, 35306734632, -555682818080, -2425630962790, -10588208505263, 166644858132571, -727427431532172, 3175319503526856, -49975467287014789 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is the rational component (with respect to the field Q(sqrt(13))) of the number A(2*n)*2*13^(floor((n+1)/3)/2), where 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).

The basic sequence 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).

We note that s(1) + s(3) + s(9) = s(1)^(-1) + s(3)^(-1) + s(9)^(-1) = sqrt((13-3*sqrt(13))/2).

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

Table of n, a(n) for n=0..20.

CROSSREFS

Cf. A019698, A216605, A216486, A216508, A216597, A216540, A161905, A216450, A216801, A216861, A217548, A217549, A211988.

Sequence in context: A269912 A042117 A179885 * A335734 A256292 A042877

Adjacent sequences:  A217545 A217546 A217547 * A217549 A217550 A217551

KEYWORD

sign

AUTHOR

Roman Witula, Oct 06 2012

STATUS

approved

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Last modified July 9 14:56 EDT 2020. Contains 335543 sequences. (Running on oeis4.)