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 A296377 Natural numbers y such that 7y^2 = x^2 + x + 1 has a solution in natural numbers. 2
 1, 7, 247, 1777, 62737, 451351, 15934951, 114641377, 4047414817, 29118458407, 1028027428567, 7395973794001, 261114919441201, 1878548225217847, 66322161510636487, 477143853231539137, 16845567908782226497, 121192660172585722951, 4278707926669174893751 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Given explicitly as the denominators of the convergents to the continued fractions [2,(1,1,1,4)^i,5,(1,1,1,4)^{i-1},1,2] (for n odd and i = (n-1)/2) and [2,(1,1,1,4)^i,1,1,2,(1,4,1,1)^i,1] (for n even and i = n/2 - 1). LINKS Colin Barker, Table of n, a(n) for n = 1..832 Index entries for linear recurrences with constant coefficients, signature (0,254,0,-1). FORMULA Recurrence: a(n) = 255*a(n-2) - 255*a(n-4) + a(n-6). From Colin Barker, Dec 11 2017: (Start) G.f.: x*(1-x)*(1+8*x+x^2) / ((1-16*x+x^2)*(1+16*x+x^2)). a(n) = 254*a(n-2) - a(n-4) for n>4. (End) EXAMPLE For n = 3 the pair is (x,y) = (653,247). PROG (PARI) Vec(x*(1-x)*(1+8*x+x^2) / ((1-16*x+x^2)*(1+16*x+x^2)) + O(x^30)) \\ Colin Barker, Dec 13 2017 CROSSREFS Cf. A296376. Sequence in context: A200961 A086214 A133589 * A223630 A203158 A227414 Adjacent sequences:  A296374 A296375 A296376 * A296378 A296379 A296380 KEYWORD nonn,easy AUTHOR Jeffrey Shallit, Dec 11 2017 STATUS approved

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Last modified November 14 22:45 EST 2019. Contains 329135 sequences. (Running on oeis4.)