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
Links
- Colin Barker, Table of n, a(n) for n = 1..800
- Index entries for linear recurrences with constant coefficients, signature (16,-1).
Crossrefs
Programs
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Magma
I:=[2,34]; [n le 2 select I[n] else 16*Self(n-1)-Self(n-2): n in [1..30]];
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Mathematica
LinearRecurrence[{16, -1}, {2, 34}, 30] -
PARI
Vec(x*(2+2*x)/(1-16*x+x^2) + O(x^50)) \\ Colin Barker, May 14 2016
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