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A273054 Numbers n such that 19*n^2 + 20 is a square. 2

%I #12 Sep 08 2022 08:46:16

%S 4,22,1382,7484,469876,2544538,159756458,865135436,54316725844,

%T 294143503702,18467527030502,100007926123244,6278904873644836,

%U 34002400738399258,2134809189512213738,11560716243129624476,725828845529279026084,3930609520263333922582

%N Numbers n such that 19*n^2 + 20 is a square.

%H Colin Barker, <a href="/A273054/b273054.txt">Table of n, a(n) for n = 1..750</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,340,0,-1).

%F G.f.: 2*x*(2 + 11*x + 11*x^2 + 2*x^3)/(1 - 340*x^2 + x^4).

%F a(n) = 340*a(n-2) - a(n-4), for n>3.

%t LinearRecurrence[{0, 340, 0, -1}, {4, 22, 1382, 7484}, 30]

%o (Magma) I:=[4,22,1382,7484]; [n le 4 select I[n] else 340*Self(n-2)-Self(n-4): n in [1..30]];

%o (PARI) x='x+O('x^99); Vec(2*x*(2+11*x+11*x^2+2*x^3)/(1-340*x^2+x^4)) \\ _Altug Alkan_, May 14 2016

%Y Cf. similar sequences listed in A273052.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, May 14 2016

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Last modified March 28 08:19 EDT 2024. Contains 371236 sequences. (Running on oeis4.)