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 A013655 a(n) = F(n+1) + L(n), where F(n) and L(n) are Fibonacci and Lucas numbers, respectively. 23
 3, 2, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555, 898, 1453, 2351, 3804, 6155, 9959, 16114, 26073, 42187, 68260, 110447, 178707, 289154, 467861, 757015, 1224876, 1981891, 3206767, 5188658, 8395425, 13584083, 21979508, 35563591, 57543099, 93106690, 150649789, 243756479 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Apart from initial term, same as A001060. Pisano period lengths same as for A001060. - R. J. Mathar, Aug 10 2012 The beginning of this sequence is the only sequence of four consecutive primes in a Fibonacci-type sequence. - Franklin T. Adams-Watters, Mar 21 2015 LINKS Mark W. Coffey, James L. Hindmarsh, Matthew C. Lettington, John Pryce, On Higher Dimensional Interlacing Fibonacci Sequences, Continued Fractions and Chebyshev Polynomials, arXiv:1502.03085 [math.NT], 2015 (see p. 31). Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (1,1) FORMULA a(n) = A000045(n+1) + A000032(n). a(n) = a(n-1) + a(n-2). a(n) = F(n+3) - F(n-2) for n>1, where F=A000045. - Gerald McGarvey, Jul 10 2004 a(n) = 2*F(n-3) + F(n) for n>1. - Zerinvary Lajos, Oct 05 2007 G.f.: (3-x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008 a(n) = Sum_{k = n-3..n+1} F(k). - Gary Detlefs, Dec 30 2012 a(n) = ((3*sqrt(5)+1)*(((1+sqrt(5))/2)^n)+(3*sqrt(5)-1)*(((1-sqrt(5))/2)^n))/(2*sqrt(5)). - Bogart B. Strauss, Jul 19 2013 a(n) = F(n+3) + F(n-3) - 3*F(n) for n>1. - Bruno Berselli, Dec 29 2016 MAPLE with(combinat): a:=n->2*fibonacci(n-1)+fibonacci(n+2): seq(a(n), n=0..40); # Zerinvary Lajos, Oct 05 2007 MATHEMATICA LinearRecurrence[{1, 1}, {3, 2}, 40] (* or *) Table[Fibonacci[n + 1] + LucasL[n], {n, 0, 40}] (* or *) Table[Fibonacci[n + 3] + Fibonacci[n - 3] - 3*Fibonacci[n], {n, 2, 40}] (* Bruno Berselli, Dec 30 2016 *) PROG (MAGMA) [2*Fibonacci(n-3)+Fibonacci(n): n in [2..41]]; // Vincenzo Librandi, Apr 16 2011 (MAGMA) [GeneralizedFibonacciNumber(3, 2, n): n in [0..39]]; // Arkadiusz Wesolowski, Mar 16 2016 (PARI) a(n)=([0, 1; 1, 1]^n*[3; 2])[1, 1] \\ Charles R Greathouse IV, Sep 24 2015 (PARI) a(n)=2*fibonacci(n-3) + fibonacci(n) \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A000045, A001060. Sequence in context: A110338 A171018 A239260 * A223701 A220519 A094894 Adjacent sequences:  A013652 A013653 A013654 * A013656 A013657 A013658 KEYWORD nonn,easy AUTHOR EXTENSIONS Definition corrected by Gary Detlefs, Dec 30 2012 STATUS approved

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