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 A237133 Values of x in the solutions to x^2 - 3xy + y^2 + 19 = 0, where 0 < x < y. 4
 4, 5, 7, 11, 17, 28, 44, 73, 115, 191, 301, 500, 788, 1309, 2063, 3427, 5401, 8972, 14140, 23489, 37019, 61495, 96917, 160996, 253732, 421493, 664279, 1103483, 1739105, 2888956, 4553036, 7563385, 11920003, 19801199, 31206973, 51840212, 81700916, 135719437 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding values of y are given by a(n+2). Positive values of x (or y) satisfying x^2 - 18xy + y^2 + 1216 = 0. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1). FORMULA a(n) = 3*a(n-2)-a(n-4). G.f.: -x*(x-1)*(4*x^2+9*x+4) / ((x^2-x-1)*(x^2+x-1)). a(n) = (1/2) * (F(n+4) + (-1)^n*F(n-5)), n>4, with F the Fibonacci numbers (A000045). - Ralf Stephan, Feb 05 2014 EXAMPLE 11 is in the sequence because (x, y) = (11, 28) is a solution to x^2 - 3xy + y^2 + 19 = 0. MATHEMATICA LinearRecurrence[{0, 3, 0, -1}, {4, 5, 7, 11}, 40] (* Harvey P. Dale, Dec 15 2014 *) PROG (PARI) Vec(-x*(x-1)*(4*x^2+9*x+4)/((x^2-x-1)*(x^2+x-1)) + O(x^100)) CROSSREFS Cf. A001519, A005248, A055819, A237132, A218735. Sequence in context: A283485 A184778 A240118 * A253584 A062709 A242212 Adjacent sequences:  A237130 A237131 A237132 * A237134 A237135 A237136 KEYWORD nonn,easy AUTHOR Colin Barker, Feb 04 2014 STATUS approved

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)