|
| |
| |
|
|
|
72, 264, 584, 1032, 1608, 2312, 3144, 4104, 5192, 6408, 7752, 9224, 10824, 12552, 14408, 16392, 18504, 20744, 23112, 25608, 28232, 30984, 33864, 36872, 40008, 43272, 46664, 50184, 53832, 57608, 61512, 65544, 69704, 73992, 78408, 82952
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The identity (16*n^2+1)^2-(64*n^2+8)*(2*n)^2 = 1 can be written as A108211(n)^2-a(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
| a(1)=72, a(2)=264, a(3)=584, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Nov 16 2011
G.f: x*(72+48*x+8*x^2)/(1-x)^3. - Vincenzo Librandi, Feb 08 2012
|
|
|
MATHEMATICA
| 64Range[40]^2+8 (* or *) LinearRecurrence[{3, -3, 1}, {72, 264, 584}, 40] (* From Harvey P. Dale, Nov 16 2011 *)
|
|
|
PROG
| (MAGMA) I:=[72, 264, 584]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 08 2012
(PARI) for(n=1, 40, print1(64*n^2 + 8", ")); \\ Vincenzo Librandi, Feb 08 2012
|
|
|
CROSSREFS
| Cf. A005843, A108211.
Sequence in context: A064716 A073412 A019507 * A165139 A004007 A173546
Adjacent sequences: A158485 A158486 A158487 * A158489 A158490 A158491
|
|
|
KEYWORD
| nonn,easy,changed
|
|
|
AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 20 2009
|
|
|
EXTENSIONS
| Comment rewritten by Bruno Berselli, Nov 16 2011
|
| |
|
|
