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 A163348 a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 1, a(1) = 7. 1
 1, 7, 35, 161, 721, 3199, 14147, 62489, 275905, 1218007, 5376707, 23734193, 104768209, 462469903, 2041441955, 9011362409, 39778080769, 175588947751, 775087121123, 3421400092481, 15102790707025, 66666943594783 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A111566. Third binomial transform of A143095. Inverse binomial transform of A081180 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 (6,-7). FORMULA a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 1, a(1) = 7. a(n) = ((1+2*sqrt(2))*(3+sqrt(2))^n + (1-2*sqrt(2))*(3-sqrt(2))^n)/2. G.f.: (1+x)/(1-6*x+7*x^2). E.g.f.: exp(3*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 19 2016 a(n) = A081179(n)+A081179(n+1). - R. J. Mathar, Feb 04 2021 MATHEMATICA LinearRecurrence[{6, -7}, {1, 7}, 50] (* G. C. Greubel, Dec 19 2016 *) PROG (MAGMA) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((1+2*r)*(3+r)^n+(1-2*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009 (PARI) Vec((1+x)/(1-6*x+7*x^2) + O(x^50)) \\ G. C. Greubel, Dec 19 2016 CROSSREFS Cf. A111566, A143095 (1,4,2,8,4,16,...), A081180. Sequence in context: A005003 A243382 A242577 * A291237 A037099 A055421 Adjacent sequences:  A163345 A163346 A163347 * A163349 A163350 A163351 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 STATUS approved

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Last modified April 13 10:24 EDT 2021. Contains 342935 sequences. (Running on oeis4.)