|
| |
|
|
A157826
|
|
103680000n^2 - 194428800n + 91152001.
|
|
3
| |
|
|
403201, 117014401, 440985601, 972316801, 1711008001, 2657059201, 3810470401, 5171241601, 6739372801, 8514864001, 10497715201, 12687926401, 15085497601, 17690428801, 20502720001, 23522371201, 26749382401, 30183753601
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The identity (103680000*n^2-194428800*n+91152001)^2-(3600*n^2-6751*n+3165)*(1728000*n-1620240)^2=1 can be written as a(n)^2-A157824(n)*A157825(n)^2=1.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
Index to sequences with 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*(-403201-115804798*x-91152001*x^2)/(x-1)^3.
|
|
|
MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {403201, 117014401, 440985601}, 40]
|
|
|
PROG
| (MAGMA) I:=[403201, 117014401, 440985601]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 103680000*n^2 - 194428800*n + 91152001.
|
|
|
CROSSREFS
| Cf. A157824, A157825.
Sequence in context: A190837 A205094 A096890 * A186606 A204764 A043609
Adjacent sequences: A157823 A157824 A157825 * A157827 A157828 A157829
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 07 2009
|
| |
|
|
