|
| |
| |
|
|
|
39, 159, 359, 639, 999, 1439, 1959, 2559, 3239, 3999, 4839, 5759, 6759, 7839, 8999, 10239, 11559, 12959, 14439, 15999, 17639, 19359, 21159, 23039, 24999, 27039, 29159, 31359, 33639, 35999, 38439, 40959, 43559, 46239, 48999, 51839, 54759
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The identity (40*n^2-1)^2-(400*n^2-20)*(2*n)^2 = 1 can be written as a(n)^2-A158597(n)*A005843(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
| G.f.: x*(-39-42*x+x^2)/(x-1)^3.
a(n)= 3*a(n-1) -3*a(n-2) +a(n-3).
|
|
|
MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {39, 159, 359}, 50] (* Vincenzo Librandi, Feb 16 2012 *)
|
|
|
PROG
| (MAGMA) I:=[39, 159, 359]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 16 2012
(PARI) for(n=1, 40, print1(40*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 16 2012
|
|
|
CROSSREFS
| Cf. A005843, A158597.
Sequence in context: A072253 A128826 A158593 * A105838 A193228 A124619
Adjacent sequences: A158595 A158596 A158597 * A158599 A158600 A158601
|
|
|
KEYWORD
| nonn,easy,changed
|
|
|
AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 22 2009
|
|
|
EXTENSIONS
| Comment rewritten, formula replaced by R. J. Mathar, Oct 28 2009
|
| |
|
|
