|
| |
|
|
A156843
|
|
279841n^2 - 165048n + 24335.
|
|
4
|
|
|
|
24335, 139128, 813603, 2047760, 3841599, 6195120, 9108323, 12581208, 16613775, 21206024, 26357955, 32069568, 38340863, 45171840, 52562499, 60512840, 69022863, 78092568, 87721955, 97911024, 108659775, 119968208, 131836323
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
The identity (279841*n^2-165048*n+24335)^2-(529*n^2-312*n+46)*(12167*n-3588)^2=1 can be written as a(n)^2-A156841(n)*A156846(n)^2=1 for n>0.
|
|
|
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).
G.f.: (24335+66123*x+469224*x^2)/(1-x)^3.
|
|
|
MATHEMATICA
|
LinearRecurrence[{3, -3, 1}, {24335, 139128, 813603}, 40]
|
|
|
PROG
|
(MAGMA) I:=[24335, 139128, 813603]; [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)= 279841*n^2-165048*n+24335 \\ Charles R Greathouse IV, Dec 23 2011
|
|
|
CROSSREFS
|
Cf. A156841, A156846, A156849.
Sequence in context: A140923 A208622 A025041 * A156844 A174754 A206682
Adjacent sequences: A156840 A156841 A156842 * A156844 A156845 A156846
|
|
|
KEYWORD
|
nonn,easy,changed
|
|
|
AUTHOR
|
Vincenzo Librandi, Feb 17 2009
|
|
|
EXTENSIONS
|
Edited by Charles R Greathouse IV, Jul 25 2010
|
|
|
STATUS
|
approved
|
| |
|
|
