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A307173 Second class of all proper positive solutions y2(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9. 2
1, 20, 319, 5084, 81025, 1291316, 20580031, 327989180, 5227246849, 83307960404, 1327700119615, 21159893953436, 337230603135361, 5374529756212340, 85655245496262079, 1365109398183980924, 21756095125447432705, 346732412608974942356, 5525962506618151644991 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The corresponding x2 solutions are given in A307172.

See A307172 for details.

LINKS

Table of n, a(n) for n=1..19.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (16,-1).

FORMULA

G.f.: x*(1 + 4*x)/(1 - 16*x + x^2).

a(n) = -4*S(n, 16) + 65*S(n-1, 16) for n >= 1, with S(n,16) = A077412(n).

a(n) = sqrt((A307172(n)^2 - 9)/7) for n >= 1.

CROSSREFS

Cf. A077421, A307168, A307169, A307172.

Sequence in context: A054621 A111778 A024387 * A101310 A229775 A159648

Adjacent sequences:  A307170 A307171 A307172 * A307174 A307175 A307176

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Mar 28 2019

STATUS

approved

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Last modified November 17 13:33 EST 2019. Contains 329230 sequences. (Running on oeis4.)