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 A164038 Expansion of (5-19*x)/(1-10*x+23*x^2). 3
 5, 31, 195, 1237, 7885, 50399, 322635, 2067173, 13251125, 84966271, 544886835, 3494644117, 22414043965, 143763624959, 922113238395, 5914569009893, 37937085615845, 243335768930911, 1560804720144675, 10011324516035797 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Binomial transform of A161731 without initial 1. Fifth binomial transform of A164095. Inverse binomial transform of A164110. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 from Vincenzo Librandi) 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) = 5, a(1) = 31. G.f.: (5-19*x)/(1-10*x+23*x^2). a(n) = ((5+3*sqrt(2))*(5+sqrt(2))^n + (5-3*sqrt(2))*(5-sqrt(2))^n)/2. E.g.f: (5*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))*exp(5*x). - G. C. Greubel, Sep 08 2017 MAPLE a:=series((5-19*x)/(1-10*x+23*x^2), x=0, 20): seq(coeff(a, x, n), n=0..19); # Paolo P. Lava, Mar 28 2019 MATHEMATICA LinearRecurrence[{10, -23}, {5, 31}, 50] (* or *) CoefficientList[Series[(5 - 19*x)/(1 - 10*x + 23*x^2), {x, 0, 50}], x] (* G. C. Greubel, Sep 08 2017 *) PROG (MAGMA) Z:= PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((5+3*r)*(5+r)^n+(5-3*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 10 2009 (PARI) Vec((5-19*x)/(1-10*x+23*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012 CROSSREFS Cf. A161731, A164095, A164110. Sequence in context: A015540 A014987 A108079 * A260782 A084235 A288688 Adjacent sequences:  A164035 A164036 A164037 * A164039 A164040 A164041 KEYWORD nonn,easy AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Aug 10 2009 STATUS approved

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Last modified February 20 07:54 EST 2020. Contains 332069 sequences. (Running on oeis4.)