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A156868
a(n) = 729000*n + 180.
4
729180, 1458180, 2187180, 2916180, 3645180, 4374180, 5103180, 5832180, 6561180, 7290180, 8019180, 8748180, 9477180, 10206180, 10935180, 11664180, 12393180, 13122180, 13851180, 14580180, 15309180, 16038180, 16767180, 17496180
OFFSET
1,1
COMMENTS
The identity (32805000*n^2 + 16200*n + 1)^2 - (2025*n^2 + n)*(729000*n + 180)^2 = 1 can be written as A157081(n)^2 - A156856(n)*a(n)^2 = 1.
FORMULA
a(n) = 2*a(n-1) - a(n-2).
G.f.: 180*x*(4051-x)/(1-x)^2.
E.g.f.: 180*(-1 + (1 + 4050*x)*exp(x)). - G. C. Greubel, Jan 28 2022
MATHEMATICA
LinearRecurrence[{2, -1}, {729180, 1458180}, 40]
729000*Range[30]+180 (* Harvey P. Dale, Jan 11 2014 *)
PROG
(Magma) I:=[729180, 1458180]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..30]];
(PARI) a(n)=729000*n+180 \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [180*(4050*n + 1) for n in (1..40)] # G. C. Greubel, Jan 28 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 17 2009
STATUS
approved