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A156867
a(n) = 729000*n - 180.
4
728820, 1457820, 2186820, 2915820, 3644820, 4373820, 5102820, 5831820, 6560820, 7289820, 8018820, 8747820, 9476820, 10205820, 10934820, 11663820, 12392820, 13121820, 13850820, 14579820, 15308820, 16037820, 16766820, 17495820
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 A157080(n)^2 - A156855(n)*a(n)^2 = 1.
FORMULA
a(n) = 2*a(n-1) - a(n-2).
G.f.: x*(728820+180*x)/(1-x)^2.
E.g.f.: 180*(1 - (1 - 4050*x)*exp(x)). - G. C. Greubel, Jan 28 2022
MATHEMATICA
LinearRecurrence[{2, -1}, {728820, 1457820}, 40]
PROG
(Magma) I:=[728820, 1457820]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
(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