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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). 1
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.

LINKS

Colin Barker, Table of n, a(n) for n = 0..550

Index entries for linear recurrences with constant coefficients, signature (55,-330,462,-165,11).

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

Sequence in context: A176267 A105715 A111821 * A068666 A082780 A063855

Adjacent sequences:  A275543 A275544 A275545 * A275547 A275548 A275549

KEYWORD

nonn,easy

AUTHOR

Kai Wang, Aug 01 2016

STATUS

approved

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Last modified July 5 00:40 EDT 2020. Contains 335457 sequences. (Running on oeis4.)