A156771 a(n) = 729*n - 531.

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

Offset: 1

Author

Vincenzo Librandi, Feb 15 2009

Keywords

• nonn
• easy

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

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A156677, A156773.

Programs

Magma

I:=[198, 927]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

Mathematica

LinearRecurrence[{2,-1},{198,927},40]

PARI

a(n)=729*n-531 \\ Charles R Greathouse IV, Dec 23 2011

Sage

[9*(81*n -59) for n in [1..50]] # G. C. Greubel, Jun 19 2021

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