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 A163616 a(n) = ((1 + 3*sqrt(2))*(5 + sqrt(2))^n + (1 - 3*sqrt(2))*(5 - sqrt(2))^n)/2. 3
 1, 11, 87, 617, 4169, 27499, 179103, 1158553, 7466161, 48014891, 308427207, 1979929577, 12705470009, 81516319819, 522937387983, 3354498523993, 21517425316321, 138020787111371, 885307088838327, 5678592784821737 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A163615. Fifth binomial transform of A163864. Inverse binomial transform of A081183 without initial 0. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (10,-23). FORMULA a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 11. G.f.: (1+x)/(1-10*x+23*x^2). E.g.f.: exp(5*x)*( cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 30 2017 a(n) = A081182(n)+A081182(n+1). - R. J. Mathar, Jul 01 2022 MATHEMATICA CoefficientList[Series[(1 + x)/(1 - 10 x + 23 x^2), {x, 0, 20}], x] (* Wesley Ivan Hurt, Jun 14 2014 *) LinearRecurrence[{10, -23}, {1, 11}, 50] (* G. C. Greubel, Jul 30 2017 *) PROG (Magma) Z:= PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((1+3*r)*(5+r)^n+(1-3*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 06 2009 (PARI) x='x+O('x^50); Vec((1+x)/(1-10*x+23*x^2)) \\ G. C. Greubel, Jul 30 2017 CROSSREFS Cf. A163615, A163864, A081183. Sequence in context: A232078 A016222 A081013 * A224182 A119383 A001278 Adjacent sequences: A163613 A163614 A163615 * A163617 A163618 A163619 KEYWORD nonn,easy AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Aug 06 2009 STATUS approved

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Last modified August 2 19:53 EDT 2024. Contains 374875 sequences. (Running on oeis4.)