A307173 Second class of all proper positive solutions y2(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9.

1, 20, 319, 5084, 81025, 1291316, 20580031, 327989180, 5227246849, 83307960404, 1327700119615, 21159893953436, 337230603135361, 5374529756212340, 85655245496262079, 1365109398183980924, 21756095125447432705, 346732412608974942356, 5525962506618151644991

Offset: 1

Author

Wolfdieter Lang, Mar 28 2019

Keywords

• nonn
• easy

Comments

The corresponding x2 solutions are given in A307172.

See A307172 for details.

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (16,-1).

Crossrefs

Cf. A077421, A307168, A307169, A307172.

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.