A157804 a(n) = 1482401250*n^2 - 2793393900*n + 1315947601.

4954951, 1658764801, 6277377151, 13860792001, 24409009351, 37922029201, 54399851551, 73842476401, 96249903751, 121622133601, 149959165951, 181261000801, 215527638151, 252759078001, 292955320351, 336116365201, 382242212551

Offset

1,1

Comments

The identity (1482401250*n^2 - 2793393900*n + 1315947601)^2 - (27225*n^2 - 51302*n + 24168)*(8984250*n - 8464830)^2 = 1 can be written as a(n)^2 - A157802(n)*A157803(n)^2 = 1.

This is the case s=165 and r=25651 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, 27224, ... - 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*(4954951 + 1643899948*x + 1315947601*x^2)/(1 - x)^3.

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

Mathematica

LinearRecurrence[{3, -3, 1}, {4954951, 1658764801, 6277377151}, 30]

Prog

(Magma) I:=[4954951, 1658764801, 6277377151]; [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 - 2793393900*n + 1315947601;

Crossrefs

Cf. A157802, A157803.

Sequence in context: A143687 A244266 A222976 * A151646 A210318 A359296

Adjacent sequences: A157801 A157802 A157803 * A157805 A157806 A157807

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved