|
| |
|
|
A156721
|
|
57122n^2 - 47320n + 9801.
|
|
3
| |
|
|
19603, 143649, 381939, 734473, 1201251, 1782273, 2477539, 3287049, 4210803, 5248801, 6401043, 7667529, 9048259, 10543233, 12152451, 13875913, 15713619, 17665569, 19731763, 21912201, 24206883, 26615809, 29138979
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
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-A156639(n)*A156627(n)^2=1.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..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).
G.f.: x*(-19603-84840*x-9801*x^2)/(x-1)^3.
|
|
|
MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {19603, 143649, 381939}, 40]
|
|
|
PROG
| (MAGMA) I:=[19603, 143649, 381939]; [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)=57122n^2-47320*n+9801 \\ Charles R Greathouse IV, Dec 23 2011
|
|
|
CROSSREFS
| Cf. A156627, A156639.
Sequence in context: A093219 A184493 A069369 * A174760 A115472 A022234
Adjacent sequences: A156718 A156719 A156720 * A156722 A156723 A156724
|
|
|
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
|
| |
|
|
