login
A157814
a(n) = 27225*n^2 - 2*n.
3
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
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.
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
Sequence in context: A224466 A127411 A268358 * A216943 A250852 A157820
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 07 2009
STATUS
approved