OFFSET
1,2
LINKS
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
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
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