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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A165225 a(0)=1, a(1)=5, a(n) = 10*a(n-1) - 5*a(n-2) for n > 1. 6
 1, 5, 45, 425, 4025, 38125, 361125, 3420625, 32400625, 306903125, 2907028125, 27535765625, 260822515625, 2470546328125, 23401350703125, 221660775390625, 2099601000390625, 19887706126953125, 188379056267578125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sum_{k=1..(m-1)/2} tan^(2n) (k*Pi/m) is an integer when m >= 3 is an odd integer (see AMM and Crux Mathematicorum links); twice this sequence is the particular case m = 5. - Bernard Schott, Apr 25 2022 LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000. 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. D. J. Smeenk, Problem 3452, Crux Mathematicorum, Vol. 35, No. 5 (2009), pp. 325 and 327; Solution to Problem 3452 by Roy Barbara, ibid., Vol. 36, No. 5 (2010), pp. 341-342. Index entries for linear recurrences with constant coefficients, signature (10,-5). FORMULA Limit_{n->oo} a(n+1)/a(n) = 5 + 2*sqrt(5) = 9.47213595... G.f.: (1-5x)/(1-10x+5x^2). a(n) = ((5 - 2*sqrt(5))^n + (5 + 2*sqrt(5))^n)/2. - Klaus Brockhaus, Sep 25 2009 a(n) = (tan(Pi/5)^(2*n) + tan(2*Pi/5)^(2*n))/2 (Smeenk, 2009). - Amiram Eldar, Apr 03 2022 MATHEMATICA LinearRecurrence[{10, -5}, {1, 5}, 30] (* Harvey P. Dale, Dec 23 2019 *) CROSSREFS Cf. A019934, A019970. Similar with: A000244 (m=3), 2*this sequence (m=5), A108716 (m=7), A353410 (m=9), A275546 (m=11), A353411 (m=13). Sequence in context: A022022 A058410 A005979 * A121272 A346580 A054318 Adjacent sequences:  A165222 A165223 A165224 * A165226 A165227 A165228 KEYWORD easy,nonn AUTHOR Philippe Deléham, Sep 09 2009 EXTENSIONS More terms from Klaus Brockhaus, Sep 25 2009 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 August 7 12:01 EDT 2022. Contains 355985 sequences. (Running on oeis4.)