|
| |
|
|
A156735
|
|
57122n^2 + 47320n + 9801.
|
|
3
| |
|
|
9801, 114243, 332929, 665859, 1113033, 1674451, 2350113, 3140019, 4044169, 5062563, 6195201, 7442083, 8803209, 10278579, 11868193, 13572051, 15390153, 17322499, 19369089, 21529923, 23805001, 26194323, 28697889, 31315699
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| The identity (57122*n^2+47320*n+9801)^2-(169*n^2+140*n+29)*(4394*n+1820)^2=1 can be written as a(n)^2-A156640(n)*A156636(n)^2=1.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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).
|
|
|
MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {9801, 114243, 332929}, 50]
|
|
|
PROG
| (MAGMA) I:=[9801, 114243, 332929]; [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)= 57122*n^2+47320*n+9801 \\ Charles R Greathouse IV, Dec 23 2011
|
|
|
CROSSREFS
| Cf. A156636, A156640, A156718.
Sequence in context: A145209 A035911 A069333 * A113937 A036353 A174769
Adjacent sequences: A156732 A156733 A156734 * A156736 A156737 A156738
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 15 2009
|
|
|
EXTENSIONS
| Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Jul 25 2010
|
| |
|
|
