A157770 1482401250n^2 - 2134548900n + 768398401.

116250751, 2428905601, 7706362951, 15948622801, 27155685151, 41327550001, 58464217351, 78565687201, 101631959551, 127663034401, 156658911751, 188619591601, 223545073951, 261435358801, 302290446151, 346110336001, 392895028351, 442644523201, 495358820551

Offset

1,1

Comments

The identity (1482401250*n^2-2134548900*n+768398401)^2-(27225*n^2-39202*n+14112) *(8984250*n-6468330)^2=1 can be written as a(n)^2-A157768(n)*A157769(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*(-116250751-2080153348*x-768398401*x^2)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {116250751, 2428905601, 7706362951}, 30]

Prog

(Magma)  I:=[116250751, 2428905601, 7706362951]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..20]];
(PARI) a(n)=1482401250*n^2-2134548900*n+768398401 \\ Charles R Greathouse IV, Dec 27 2011

Crossrefs

Cf. A157768, A157769.

Sequence in context: A216010 A206751 A206062 * A195282 A186804 A344632

Adjacent sequences: A157767 A157768 A157769 * A157771 A157772 A157773

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 06 2009

Status

approved