|
|
A156771
|
|
a(n) = 729*n - 531.
|
|
3
|
|
|
198, 927, 1656, 2385, 3114, 3843, 4572, 5301, 6030, 6759, 7488, 8217, 8946, 9675, 10404, 11133, 11862, 12591, 13320, 14049, 14778, 15507, 16236, 16965, 17694, 18423, 19152, 19881, 20610, 21339, 22068, 22797, 23526, 24255, 24984, 25713
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The identity (6561*n^2 - 9558*n + 3482)^2 - (81*n^2 - 118*n + 43)*(729*n - 531)^2 = 1 can be written as A156773(n)^2 - A156677(n)*a(n)^2 = 1.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*a(n-1) - a(n-2).
G.f.: x*(198 + 531*x)/(1-x)^2.
E.g.f.: 9*(59 - (59 - 81*x)*exp(x)). - G. C. Greubel, Jun 19 2021
|
|
MATHEMATICA
|
LinearRecurrence[{2, -1}, {198, 927}, 40]
|
|
PROG
|
(Magma) I:=[198, 927]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(Sage) [9*(81*n -59) for n in [1..50]] # G. C. Greubel, Jun 19 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|