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 A163350 a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 6. 4
 1, 6, 34, 188, 1028, 5592, 30344, 164464, 890896, 4824672, 26124832, 141453248, 765878336, 4146681216, 22451153024, 121555687168, 658129355008, 3563255219712, 19292230787584, 104452273224704, 565526954771456 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A102285. Fourth binomial transform of A163403. Inverse binomial transform of A163346. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (8, -14). FORMULA a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 6. a(n) = ((1+sqrt(2))*(4+sqrt(2))^n+(1-sqrt(2))*(4-sqrt(2))^n)/2. G.f.: (1-2*x)/(1-8*x+14*x^2). E.g.f.: exp(4*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 19 2016 MATHEMATICA LinearRecurrence[{8, -14}, {1, 6}, 30] (* Harvey P. Dale, May 08 2014 *) PROG (Magma) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((1+r)*(4+r)^n+(1-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009 (PARI) Vec((1-2*x)/(1-8*x+14*x^2) + O(x^50)) \\ G. C. Greubel, Dec 19 2016 CROSSREFS Cf. A102285, A163403, A163346. Sequence in context: A229009 A085351 A125343 * A320746 A320749 A052264 Adjacent sequences: A163347 A163348 A163349 * A163351 A163352 A163353 KEYWORD nonn,easy AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Jul 26 2009 New name from G. C. Greubel, Dec 19 2016 STATUS approved

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Last modified November 28 03:39 EST 2022. Contains 358406 sequences. (Running on oeis4.)