A157814 - OEIS

A157814

a(n) = 27225*n^2 - 2*n.

27223, 108896, 245019, 435592, 680615, 980088, 1334011, 1742384, 2205207, 2722480, 3294203, 3920376, 4600999, 5336072, 6125595, 6969568, 7867991, 8820864, 9828187, 10889960, 12006183, 13176856, 14401979, 15681552, 17015575

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The identity (1482401250*n^2-108900*n+1)^2-(27225*n^2-2*n)*(8984250*n-330)^2=1 can be written as A157816(n)^2-a(n)*A157815(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

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

G.f.: x*(27223+27227*x)/(1-x)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {27223, 108896, 245019}, 40]

PROG

(Magma) I:=[27223, 108896, 245019]; [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 - 2*n.

CROSSREFS

Cf. A157815, A157816.

Sequence in context: A224466 A127411 A268358 * A216943 A250852 A157820

Adjacent sequences: A157811 A157812 A157813 * A157815 A157816 A157817

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 07 2009

STATUS

approved