A156867 - OEIS

A156867

a(n) = 729000*n - 180.

728820, 1457820, 2186820, 2915820, 3644820, 4373820, 5102820, 5831820, 6560820, 7289820, 8018820, 8747820, 9476820, 10205820, 10934820, 11663820, 12392820, 13121820, 13850820, 14579820, 15308820, 16037820, 16766820, 17495820

(list; graph; refs; listen; history; text; internal format)

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.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (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

Cf. A156855, A156868, A157080.

Sequence in context: A204150 A321495 A234495 * A156868 A238297 A329225

Adjacent sequences: A156864 A156865 A156866 * A156868 A156869 A156870

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Feb 17 2009

STATUS

approved