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 A022113 Fibonacci sequence beginning 2, 7. 14
 2, 7, 9, 16, 25, 41, 66, 107, 173, 280, 453, 733, 1186, 1919, 3105, 5024, 8129, 13153, 21282, 34435, 55717, 90152, 145869, 236021, 381890, 617911, 999801, 1617712, 2617513, 4235225, 6852738, 11087963, 17940701, 29028664, 46969365, 75998029, 122967394 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES H. S. M. Coxeter, Introduction to Geometry, Second Edition, Wiley Classics Library Edition Published 1989, p. 172. LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (1,1). FORMULA From Colin Barker, Oct 18 2013: (Start) G.f.: -(5*x + 2)/(x^2 + x - 1). a(n) = a(n-1) + a(n-2). (End) a(n) = ((5+6*sqrt(5))/5)*((1+sqrt(5))/2)^n + ((5-6*sqrt(5))/5)*((1-sqrt(5))/2)^n starting at n=0. - Bogart B. Strauss, Oct 27 2013 a(n) = h*Fibonacci(n+k) + Fibonacci(n+k-h) with h=5, k=1. - Bruno Berselli, Feb 20 2017 a(n) = 8*F(n) + F(n-3) for F = A000045. - J. M. Bergot, Jul 14 2017 a(n) = Fibonacci(n+4) + Lucas(n-1). - Greg Dresden and Henry Sauer, Mar 04 2022 E.g.f.: 2*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 6*sqrt(5)*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Jul 18 2022 MATHEMATICA RecurrenceTable[{a[0] == 2, a[1] == 7, a[n] == a[n - 1] + a[n - 2]}, a, {n, 0, 40}] (* Bruno Berselli, Mar 12 2015 *) LinearRecurrence[{1, 1}, {2, 7}, 37] (* or *) CoefficientList[Series[-(5 x + 2)/(x^2 + x - 1), {x, 0, 36}], x] (* Michael De Vlieger, Jul 14 2017 *) PROG (Magma) a0:=2; a1:=7; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]]; // Bruno Berselli, Feb 12 2013 (PARI) a(n)=8*fibonacci(n)+fibonacci(n-3) \\ Charles R Greathouse IV, Jul 14 2017 (PARI) a(n)=([0, 1; 1, 1]^n*[2; 7])[1, 1] \\ Charles R Greathouse IV, Jul 14 2017 CROSSREFS Cf. A000032. A000045. Sequence in context: A165995 A287575 A267212 * A041643 A041395 A042345 Adjacent sequences: A022110 A022111 A022112 * A022114 A022115 A022116 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified March 28 05:31 EDT 2023. Contains 361577 sequences. (Running on oeis4.)