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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.)