|
|
A157757
|
|
a(n) = 2809*n^2 - 4618*n + 1898.
|
|
3
|
|
|
89, 3898, 13325, 28370, 49033, 75314, 107213, 144730, 187865, 236618, 290989, 350978, 416585, 487810, 564653, 647114, 735193, 828890, 928205, 1033138, 1143689, 1259858, 1381645, 1509050, 1642073, 1780714, 1924973, 2074850
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The identity (15780962*n^2-25943924*n+10662963)^2-(2809*n^2-4618*n+1898)*(297754*n-244754)^2=1 can be written as A157759(n)^2-a(n)*A157758(n)^2=1.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(-89-3631*x-1898*x^2)/(x-1)^3.
|
|
MATHEMATICA
|
LinearRecurrence[{3, -3, 1}, {89, 3898, 13325}, 40]
|
|
PROG
|
(Magma) I:=[89, 3898, 13325]; [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) = 2809*n^2 - 4618*n + 1898;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|