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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A275546 a(n) = (tan(1*Pi/11))^(2*n) + (tan(2*Pi/11))^(2*n) + (tan(3*Pi/11))^(2*n) + (tan(4*Pi/11))^(2*n) + (tan(5*Pi/11))^(2*n). 5
5, 55, 2365, 113311, 5476405, 264893255, 12813875437, 619859803695, 29985188632421, 1450508002869079, 70167091762786205, 3394273427239643839, 164195092176119969173, 7942798031108524622951, 384226104001681151724877, 18586611219134532494467151, 899111520569015285343455941, 43493755633501102693569684087, 2103973462501643822799172235773 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
(tan(1*Pi/11))^(2*n), (tan(2*Pi/11))^(2*n), (tan(3*Pi/11))^(2*n),(tan(4*Pi/11))^(2*n), (tan(5*Pi/11))^(2*n) are roots of the polynomial x^5 - 55x^4 + 330x^3 - 462x^2 + 165x - 11.
Sum_{k=1..(m-1)/2)} tan^(2n) (k*Pi/m) is an integer when m >= 3 is an odd integer (see AMM link); this sequence is the particular case m = 11. All terms are odd. - Bernard Schott, Apr 24 2022
LINKS
Michel Bataille and Li Zhou, A Combinatorial Sum Goes on Tangent, The American Mathematical Monthly, Vol. 112, No. 7 (Aug. - Sep., 2005), Problem 11044, pp. 657-659.
FORMULA
a(-2) = 141, a(-1) = 15, a(0) = 5, a(1) = 55, a(2) = 2365.
a(n) = +55*a(n-1)-330*a(n-2)+462*a(n-3)-165*a(n-4)-11*a(n-5) for n > 2.
a(n) ~ k^n where k = 48.37415... is the largest real root of x^5 - 55x^4 + 330x^3 - 462x^2 + 165x - 11. - Charles R Greathouse IV, Aug 01 2016
G.f.: (5-220*x+990*x^2-924*x^3+165*x^4) / (1-55*x+330*x^2-462*x^3+165*x^4-11*x^5). - Colin Barker, Aug 02 2016
PROG
(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 11, -165, 462, -330, 55]^n*[5; 55; 2365; 113311; 5476405])[1, 1] \\ Charles R Greathouse IV, Aug 01 2016
(PARI) Vec((5-220*x+990*x^2-924*x^3+165*x^4)/(1-55*x+330*x^2-462*x^3+165*x^4-11*x^5) + O(x^20)) \\ Colin Barker, Aug 02 2016
CROSSREFS
Similar to: A000244 (m=3), 2*A165225 (m=5), A108716 (m=7), A353410 (m=9), this sequence (m=11), A353411 (m=13).
Sequence in context: A176267 A105715 A111821 * A068666 A082780 A063855
KEYWORD
nonn,easy
AUTHOR
Kai Wang, Aug 01 2016
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)