|
|
A156866
|
|
a(n) = 729000*n - 116820.
|
|
3
|
|
|
612180, 1341180, 2070180, 2799180, 3528180, 4257180, 4986180, 5715180, 6444180, 7173180, 7902180, 8631180, 9360180, 10089180, 10818180, 11547180, 12276180, 13005180, 13734180, 14463180, 15192180, 15921180, 16650180, 17379180
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The identity (32805000*n^2 - 10513800*n + 842401)^2 - (2025*n^2 - 3401*n + 1428)*(729000*n - 116820)^2 = 1 can be written as A157079(n)^2 - A156854(n)*a(n)^2 = 1.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*a(n-1) - a(n-2).
G.f.: 180*x*(3401+649*x)/(1-x)^2.
E.g.f.: 180*(649 - (649 - 4050*x)*exp(x)). - G. C. Greubel, Jan 28 2022
|
|
MATHEMATICA
|
LinearRecurrence[{2, -1}, {612180, 1341180}, 40]
|
|
PROG
|
(Magma) I:=[612180, 1341180]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
(Sage) [180*(4050*n -649) for n in (1..40)] # G. C. Greubel, Jan 28 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|