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 A059769 Frobenius number of the subsemigroup of the natural numbers generated by successive pairs of Fibonacci numbers. 13
 1, 7, 27, 83, 239, 659, 1781, 4751, 12583, 33175, 87231, 228983, 600473, 1573655, 4122467, 10796939, 28273519, 74031979, 193835949, 507497759, 1328692751, 3478637807, 9107313407, 23843452463, 62423286769, 163426800679, 427857750891, 1120147480451 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS R. FrÃ¶berg, C. Gottlieb and R. Haggkvist, On numerical semigroups, Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number). FORMULA a(n) = (F(n)-1)*(F(n+1)-1)-1 where F(n) is the n-th Fibonacci number. G.f.: x^3*(1+4*x+5*x^2-x^4)/((1+x)*(1-3*x+x^2)*(1-x-x^2)). [Colin Barker, Feb 17 2012] a(n) = F(n)*F(n+1) - F(n+2). - Clark Kimberling, Mar 05 2016 EXAMPLE a(3)=1 because the 3rd and 4th Fibonacci numbers are 2 and 3, so a(3)=(2-1)(3-1)-1=1. Or, a(3)=1 because 1 is the largest positive integer that is not a nonnegative linear combination of 2 and 3. MATHEMATICA Table[(Fibonacci[n]-1)(Fibonacci[n+1]-1)-1, {n, 3, 28}] (* T. D. Noe, Nov 27 2006 *) f[n_]:=Fibonacci[n]; Table[f[n+1]f[n+2]-f[n+3], {n, 2, 40}] (* Clark Kimberling, Mar 05 2016 *) PROG (PARI) x='x+O('x^100); Vec(x^3*(1+4*x+5*x^2-x^4)/(1+x)/(1-3*x+x^2)/(1-x-x^2)) \\ Altug Alkan, Mar 05 2016 (MAGMA) [Fibonacci(n+1)*Fibonacci(n+2)-Fibonacci(n+3): n in [2..30]]; // Vincenzo Librandi, Mar 06 2016 CROSSREFS Cf. A000045. Sequence in context: A036597 A038092 A059823 * A135914 A213588 A305653 Adjacent sequences:  A059766 A059767 A059768 * A059770 A059771 A059772 KEYWORD nonn,easy AUTHOR Victoria A Sapko (vsapko(AT)math.unl.edu), Feb 21 2001 EXTENSIONS Corrected by T. D. Noe, Nov 27 2006 STATUS approved

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Last modified August 13 22:26 EDT 2020. Contains 336463 sequences. (Running on oeis4.)