A273052 Numbers n such that 7*n^2 + 8 is a square.

2, 34, 542, 8638, 137666, 2194018, 34966622, 557271934, 8881384322, 141544877218, 2255836651166, 35951841541438, 572973628011842, 9131626206648034, 145533045678356702, 2319397104647059198, 36964820628674590466, 589117732954146388258, 9388918906637667621662

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..800

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

Formula

O.g.f.: x*(2 + 2*x)/(1 - 16*x + x^2).

E.g.f.: 2*(1 + (3*sqrt(7)*sinh(3*sqrt(7)*x) - 7*cosh(3*sqrt(7)*x))*exp(8*x)/7). - Ilya Gutkovskiy, May 14 2016

a(n) = 16*a(n-1) - a(n-2).

a(n) = (-(8-3*sqrt(7))^n*(3+sqrt(7))-(-3+sqrt(7))*(8+3*sqrt(7))^n)/sqrt(7). - Colin Barker, May 14 2016

Mathematica

LinearRecurrence[{16, -1}, {2, 34}, 30]

Prog

(Magma) I:=[2, 34]; [n le 2 select I[n] else 16*Self(n-1)-Self(n-2): n in [1..30]];
(PARI) Vec(x*(2+2*x)/(1-16*x+x^2) + O(x^50)) \\ Colin Barker, May 14 2016

Crossrefs

Cf. Numbers n such that k*n^2+(k+1) is a square: A052530 (k=3), this sequence (k=7), A106328 (k=8), A106256 (k=12), A273053 (k=15), A273054 (k=19), A106331 (k=24).

Sequence in context: A104898 A218432 A071799 * A098704 A119298 A045585

Adjacent sequences: A273049 A273050 A273051 * A273053 A273054 A273055

Keyword

nonn,easy

Author

Vincenzo Librandi, May 14 2016

Status

approved