A273052 - OEIS

%I #21 Sep 08 2022 08:46:16

%S 2,34,542,8638,137666,2194018,34966622,557271934,8881384322,

%T 141544877218,2255836651166,35951841541438,572973628011842,

%U 9131626206648034,145533045678356702,2319397104647059198,36964820628674590466,589117732954146388258,9388918906637667621662

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

%H Colin Barker, <a href="/A273052/b273052.txt">Table of n, a(n) for n = 1..800</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-1).

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

%F 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

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

%F 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

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

%o (Magma) I:=[2,34]; [n le 2 select I[n] else 16*Self(n-1)-Self(n-2): n in [1..30]];

%o (PARI) Vec(x*(2+2*x)/(1-16*x+x^2) + O(x^50)) \\ _Colin Barker_, May 14 2016

%Y 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).

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, May 14 2016