A157802 a(n) = 27225*n^2 - 51302*n + 24168.

91, 30464, 115287, 254560, 448283, 696456, 999079, 1356152, 1767675, 2233648, 2754071, 3328944, 3958267, 4642040, 5380263, 6172936, 7020059, 7921632, 8877655, 9888128, 10953051, 12072424, 13246247, 14474520, 15757243, 17094416

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 A157804(n)^2-a(n)*A157803(n)^2=1.

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*(91 + 30191*x + 24168*x^2)/(1 - x)^3.

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

Mathematica

LinearRecurrence[{3, -3, 1}, {91, 30464, 115287}, 40]

Prog

(Magma) I:=[91, 30464, 115287]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]];
(PARI) a(n) = 27225*n^2 - 51302*n + 24168;

Crossrefs

Cf. A157803, A157804.

Sequence in context: A116507 A083828 A348088 * A214110 A119130 A195217

Adjacent sequences: A157799 A157800 A157801 * A157803 A157804 A157805

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved