A157768 27225n^2 - 39202n + 14112.

2135, 44608, 141531, 292904, 498727, 759000, 1073723, 1442896, 1866519, 2344592, 2877115, 3464088, 4105511, 4801384, 5551707, 6356480, 7215703, 8129376, 9097499, 10120072, 11197095, 12328568, 13514491, 14754864, 16049687, 17398960

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 A157770(n)^2-a(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*(-2135-38203*x-14112*x^2)/(x-1)^3.

Mathematica

Table[27225n^2-39202n+14112, {n, 50}]  (* Harvey P. Dale, Mar 26 2011 *)

Prog

(Magma) I:=[2135, 44608, 141531]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..30]];
(PARI) a(n) = 27225*n^2 - 39202*n + 14112

Crossrefs

Cf. A157769, A157770.

Sequence in context: A110024 A260068 A237070 * A067199 A064249 A206007

Adjacent sequences: A157765 A157766 A157767 * A157769 A157770 A157771

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 06 2009

Extensions

Entries checked by David Wasserman, Jun 17 2010

Status

approved