|
| |
|
|
A157506
|
|
13122n^2 + 324n + 1.
|
|
3
| |
|
|
13447, 53137, 119071, 211249, 329671, 474337, 645247, 842401, 1065799, 1315441, 1591327, 1893457, 2221831, 2576449, 2957311, 3364417, 3797767, 4257361, 4743199, 5255281, 5793607, 6358177, 6948991, 7566049, 8209351, 8878897
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The identity (13122n^2+324n+1)^2-(81n^2+2n)*(1458n+18)^2=1 can be written as a(n)^2-A177099(n)*A157505(n)^2=1 (see the Berselli's comment in A177099). - Vincenzo Librandi, Feb 04 2012
|
|
|
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*(13447+12796*x+x^2)/(1-x)^3. - Vincenzo Librandi, Feb 04 2012
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Vincenzo Librandi, Feb 04 2012
|
|
|
MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {13447, 53137, 119071}, 50] (* Vincenzo Librandi, Feb 04 2012 *)
|
|
|
PROG
| (MAGMA) I:=[13447, 53137, 119071]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 04 2012
(PARI) for(n=1, 40, print1(13122*n^2 + 324*n + 1", ")); \\ Vincenzo Librandi, Feb 03 2012
|
|
|
CROSSREFS
| Cf. A157505, A177099.
Sequence in context: A015300 A190473 A179719 * A183676 A204394 A035917
Adjacent sequences: A157503 A157504 A157505 * A157507 A157508 A157509
|
|
|
KEYWORD
| nonn,easy,changed
|
|
|
AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 02 2009
|
| |
|
|
