A157798 a(n) = 1482401250*n^2 - 658736100*n + 73180801.

896845951, 4685313601, 11438583751, 21156656401, 33839531551, 49487209201, 68099689351, 89676972001, 114219057151, 141725944801, 172197634951, 205634127601, 242035422751, 281401520401, 323732420551, 369028123201, 417288628351

Offset

1,1

Comments

The identity (1482401250*n^2 - 658736100*n + 73180801)^2 - (27225*n^2 - 12098*n + 1344)*(8984250*n - 1996170)^2 = 1 can be written as a(n)^2 - A157796(n)*A157797(n)^2 = 1.

This is the case s=165 and r=6049 of the identity (2*(s^2*n-r)^2-1)^2 - (((s^2*n-r)^2-1)/s^2)*(2*s*(s^2*n-r))^2 = 1, where ((s^2*n-r)^2-1)/s^2 is an integer if r^2 == 1 (mod s^2). Therefore, for s=165, nonnegative r values are: 1, 1574, 6049, 7624, 19601, 21176, 25651, ... - Bruno Berselli, Apr 24 2018

Links

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

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

Formula

G.f.: x*(896845951 + 1994775748*x + 73180801*x^2)/(1 - x)^3.

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

Mathematica

LinearRecurrence[{3, -3, 1}, {896845951, 4685313601, 11438583751}, 30]

Prog

(Magma) I:=[896845951, 4685313601, 11438583751]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..30]];
(PARI) a(n) = 1482401250*n^2 - 658736100*n + 73180801;

Crossrefs

Cf. A157796, A157797.

Sequence in context: A183708 A210299 A178557 * A328135 A189229 A051470

Adjacent sequences: A157795 A157796 A157797 * A157799 A157800 A157801

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved