A157838 - OEIS

A157838

3600n^2 - 6049n + 2541.

92, 4843, 16794, 35945, 62296, 95847, 136598, 184549, 239700, 302051, 371602, 448353, 532304, 623455, 721806, 827357, 940108, 1060059, 1187210, 1321561, 1463112, 1611863, 1767814, 1930965, 2101316, 2278867, 2463618, 2655569

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OFFSET

1,1

COMMENTS

The identity (103680000*n^2-174211200*n+73180801)^2-(3600*n^2-6049*n+2541)*(1728000*n-1451760)^2=1 can be written as A157840(n)^2-a(n)*A157839(n)^2=1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

G.f.: x*(-92-4567*x-2541*x^2)/(x-1)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {92, 4843, 16794}, 40]

Table[3600n^2-6049n+2541, {n, 30}] (* Harvey P. Dale, Nov 29 2022 *)

PROG

(Magma) I:=[92, 4843, 16794]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];