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 A049664 a(n) = (F(6*n+3) - 2)/32, where F=A000045 (the Fibonacci sequence). 9
 0, 1, 19, 342, 6138, 110143, 1976437, 35465724, 636406596, 11419853005, 204920947495, 3677157201906, 65983908686814, 1184033199160747, 21246613676206633, 381255012972558648, 6841343619829849032, 122762930143964723929, 2202891398971535181691 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Partial sums of Chebyshev polynomials S(n,18). LINKS G. C. Greubel, Table of n, a(n) for n = 0..750 Index entries for linear recurrences with constant coefficients, signature (19,-19,1). FORMULA G.f.: x/(1-19*x+19*x^2-x^3) = x/((1-x)*(1-18*x+x^2). a(n+1) = Sum_{k=0..n} S(k, 18), with n>=0, S(k, 18) = U(k, 9) = A049660(k+1). a(n) = 19*a(n-1) - 19*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=19. a(n) = 18*a(n-1) - a(n-2) + 1, n>=2, a(0)=0, a(1)=1. a(n+1) = (S(n+1, 18) - S(n, 18) - 1)/16, n>=0. a(n) = -1/16-(1/80)*(9-4*sqrt(5))^n*sqrt(5)+(1/32)*(9-4*sqrt(5))^n+(1/80)*sqrt(5)*(9+4 *sqrt(5))^n+(1/32)*(9+4*sqrt(5))^n. - Paolo P. Lava, Oct 03 2008 a(n) = (1/8)*Sum_{k=0..n} Fibonacci(6*k). - Gary Detlefs, Dec 07 2010 MATHEMATICA LinearRecurrence[{19, -19, 1}, {0, 1, 19}, 50] (* or *) Table[(Fibonacci[ 6*n +3] - 2)/32, {n, 0, 30}] (* G. C. Greubel, Dec 02 2017 *) PROG (PARI) a(n)=fibonacci(6*n+3)\32 \\ Charles R Greathouse IV, Oct 07 2016 (MAGMA) [(Fibonacc9(6*n+3)-2)/32: n in [0..30]]; // G. C. Greubel, Dec 02 2017 CROSSREFS Cf. A053606. Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3). Sequence in context: A142549 A049629 A162805 * A163110 A163453 A163968 Adjacent sequences:  A049661 A049662 A049663 * A049665 A049666 A049667 KEYWORD nonn,easy AUTHOR EXTENSIONS Chebyshev comments from Wolfdieter Lang, Aug 31 2004 STATUS approved

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Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)