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 A082841 a(n) = 4*a(n-1) - a(n-2) for n>1, a(0)=3, a(1)=9. 11
 3, 9, 33, 123, 459, 1713, 6393, 23859, 89043, 332313, 1240209, 4628523, 17273883, 64467009, 240594153, 897909603, 3351044259, 12506267433, 46674025473, 174189834459, 650085312363, 2426151414993, 9054520347609, 33791929975443 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS y-values in the solution to 3*x^2+6 = y^2. - Sture Sjöstedt, Nov 25 2011 Positive values of x (or y) satisfying x^2 - 4xy + y^2 + 18 = 0. - Colin Barker, Feb 04 2014 Positive values of x (or y) satisfying x^2 - 14xy + y^2 + 288 = 0. - Colin Barker, Feb 16 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (4,-1). FORMULA G.f.: (3-6*x+3x^2)/((1-x)(1-4*x+x^2)). With a=2+sqrt(3) and b=2-sqrt(3), a(n)=sqrt(3/2)(a^(n+1/2)+b^(n+1/2)). a(n) = sqrt(3(11+12*A082840(n)+4*A082840(n)^2)). a(n) = sqrt((3/2)(A003500(2n+1)+2)). a(n)-a(n-1) = 6*A001353(n). a(n) == 3 (mod 6). a(n) = 3 * A001835(n+1). MAPLE a:=proc(n) option remember; if n=0 then 3 elif n=1 then 9 else 4*a(n-1)-a(n-2); fi; end: seq(a(n), n=0..40); # Wesley Ivan Hurt, Jan 21 2017 MATHEMATICA CoefficientList[Series[(3-6 x+3 x^2)/((1-x)(1-4 x+x^2)), {x, 0, 25}], x] CROSSREFS First differences of A005320. Cf. A001834. Sequence in context: A148996 A255713 A148997 * A151038 A039648 A219261 Adjacent sequences:  A082838 A082839 A082840 * A082842 A082843 A082844 KEYWORD nonn,easy AUTHOR Mario Catalani (mario.catalani(AT)unito.it), Apr 14 2003 STATUS approved

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Last modified December 10 12:33 EST 2018. Contains 318047 sequences. (Running on oeis4.)