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 A162769 a(n) = ((1+sqrt(5))*(4+sqrt(5))^n + (1-sqrt(5))*(4-sqrt(5))^n)/2. 1
 1, 9, 61, 389, 2441, 15249, 95141, 593389, 3700561, 23077209, 143911501, 897442709, 5596515161, 34900251489, 217640345141, 1357219994749, 8463716161441, 52780309349289, 329141597018461, 2052549373305509 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A082762. Fourth binomial transform of A162962. Inverse binomial transform of A093145 without initial 0. LINKS Index entries for linear recurrences with constant coefficients, signature (8,-11). FORMULA a(n) = 8*a(n-1) - 11*a(n-2) for n > 1; a(0) = 1, a(1) = 9. G.f.: (1+x)/(1-8*x+11*x^2). a(n) = A091870(n)+A091870(n+1). - R. J. Mathar, Feb 04 2021 MATHEMATICA f[n_] := Block[{s = Sqrt@ 5}, Simplify[((1 + s)(4 + s)^n + (1 - s)(4 - s)^n)/2]]; Array[f, 21, 0] (* Or *) a[n_] := 8 a[n - 1] - 11 a[n - 2]; a[0] = 1; a[1] = 9; Array[a, 22, 0] (* Or *) CoefficientList[Series[(1 + x)/(1 - 8 x + 11 x^2), {x, 0, 21}], x] (* Robert G. Wilson v *) PROG (MAGMA) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-5); 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 19 2009 CROSSREFS Cf. A082762, A162962, A093145. Sequence in context: A001454 A243877 A200674 * A126504 A025014 A246567 Adjacent sequences:  A162766 A162767 A162768 * A162770 A162771 A162772 KEYWORD nonn,easy AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jul 13 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Jul 19 2009 STATUS approved

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Last modified May 18 18:33 EDT 2021. Contains 343998 sequences. (Running on oeis4.)