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 A018910 Pisot sequence L(4,5). 10
 4, 5, 7, 10, 15, 23, 36, 57, 91, 146, 235, 379, 612, 989, 1599, 2586, 4183, 6767, 10948, 17713, 28659, 46370, 75027, 121395, 196420, 317813, 514231, 832042, 1346271, 2178311, 3524580, 5702889, 9227467, 14930354, 24157819, 39088171, 63245988, 102334157, 165580143 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993 Index entries for linear recurrences with constant coefficients, signature (2, 0, -1). FORMULA a(n) = Fib(n+3)+2 = A020743(n-2) = A157725(n+3); a(n) = 2a(n-1) - a(n-3). G.f.: -(-4+3*x+3*x^2)/(x-1)/(x^2+x-1) = -2/(x-1)+(-x-2)/(x^2+x-1) . - R. J. Mathar, Nov 23 2007 a(n)=2+((5+2r5)/5)((1+r5)/2)^n+((5-2r5)/5)((1-r5)/2)^n, where r5 = sqrt(5). - Paolo P. Lava, Jun 10 2008 MATHEMATICA LinearRecurrence[{2, 0, -1}, {4, 5, 7}, 40] (* Jean-François Alcover, Dec 12 2016 *) PROG (PARI) pisotL(nmax, a1, a2) = {   a=vector(nmax); a[1]=a1; a[2]=a2;   for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));   a } pisotL(50, 4, 5) \\ Colin Barker, Aug 07 2016 CROSSREFS See A008776 for definitions of Pisot sequences. Sequence in context: A093517 A248858 A145018 * A022936 A057708 A032686 Adjacent sequences:  A018907 A018908 A018909 * A018911 A018912 A018913 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified November 18 05:25 EST 2017. Contains 294853 sequences.