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 A146160 Period 4: repeat [1, 4, 1, 16]. 4
 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..93. Index entries for linear recurrences with constant coefficients, signature (0,0,0,1). FORMULA Continued fraction of (8 + sqrt(78))/14. GCD(4k - k^2, 5k^2, 20k - 20k^2, 16 - 32k + 16k^2) for k = 1,2,3,... From Artur Jasinski, Oct 29 2008: (Start) a(n) = 1 when n congruent to 1 or 3 mod 4. a(n) = 4 when n congruent to 2 mod 4. a(n) = 16 when n congruent to 0 mod 4. (End) From Richard Choulet, Nov 03 2008: (Start) a(n+4) = a(n). a(n) = (9/2)*(-1)^n + (11/2) + 6*cos(Pi*n/2). O.g.f.: f(z) = a(0)+a(1)*z+... = (1+4*z+z^2+16*z^3)/(1-z^4). (End) E.g.f.: sinh(x) + 20*(sinh(x/2))^2 - 12*(sin(x/2))^2. - G. C. Greubel, Feb 03 2016 a(n) = a(-n). - Wesley Ivan Hurt, Jun 15 2016 a(n) = A109008(n)^2. - R. J. Mathar, Feb 12 2019 From Amiram Eldar, Jan 01 2023: (Start) Multiplicative with a(2) = 4, a(2^e) = 16 for e >= 2, and a(p^e) = 1 for p >= 3. Dirichlet g.f.: zeta(s)*(12/4^s+3/2^s+1). (End) MAPLE A146160:=n->[1, 4, 1, 16][(n mod 4)+1]: seq(A146160(n), n=0..100); # Wesley Ivan Hurt, Jun 15 2016 MATHEMATICA Table[GCD[4k - k^2, 5k^2, 20k - 20k^2, 16 - 32k + 16k^2], {k, 100}] PROG (Magma) &cat[[1, 4, 1, 16]^^20]; // Vincenzo Librandi, Feb 04 2016 (PARI) Vec((1+4*x+x^2+16*x^3)/(1-x^4) + O(x^100)) \\ Altug Alkan, Feb 04 2016 CROSSREFS Cf. A010156, A145996. [Artur Jasinski, Oct 29 2008] Sequence in context: A056920 A123382 A197653 * A059222 A117292 A062780 Adjacent sequences: A146157 A146158 A146159 * A146161 A146162 A146163 KEYWORD nonn,easy,mult AUTHOR Artur Jasinski, Oct 27 2008 EXTENSIONS Choulet formula adapted for offset 1 from Wesley Ivan Hurt, Jun 15 2016 STATUS approved

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Last modified September 13 22:05 EDT 2024. Contains 375910 sequences. (Running on oeis4.)