|
| |
|
|
A157653
|
|
80000n^2 - 39200n + 4801.
|
|
3
| |
|
|
45601, 246401, 607201, 1128001, 1808801, 2649601, 3650401, 4811201, 6132001, 7612801, 9253601, 11054401, 13015201, 15136001, 17416801, 19857601, 22458401, 25219201, 28140001, 31220801, 34461601, 37862401, 41423201, 45144001
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The identity (80000*n^2-39200*n+4801)^2-(100*n^2-49*n+6)*(8000*n-1960)^2=1 can be written as a(n)^2-A157651(n)*A157652(n)^2=1.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Philippe Chevanne, Pell Equation
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*(-45601-109598*x-4801*x^2)/(x-1)^3.
|
|
|
MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {45601, 246401, 607201}, 40]
|
|
|
PROG
| (MAGMA) I:=[45601, 246401, 607201]; [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) = 80000*n^2 - 39200*n + 4801.
|
|
|
CROSSREFS
| Cf. A157651, A157652.
Sequence in context: A163816 A055355 A184473 * A202915 A031841 A159725
Adjacent sequences: A157650 A157651 A157652 * A157654 A157655 A157656
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 03 2009
|
| |
|
|
