A156772 a(n) = 729*n - 198.

531, 1260, 1989, 2718, 3447, 4176, 4905, 5634, 6363, 7092, 7821, 8550, 9279, 10008, 10737, 11466, 12195, 12924, 13653, 14382, 15111, 15840, 16569, 17298, 18027, 18756, 19485, 20214, 20943, 21672, 22401, 23130, 23859, 24588, 25317, 26046

Offset: 1

Author

Vincenzo Librandi, Feb 15 2009

Keywords

• nonn
• easy

Comments

The identity (6561*n^2 - 3564*n + 485)^2 - (81*n^2 - 44*n + 6)*(729*n - 198)^2 = 1 can be written as A156774(n)^2 - A156676(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. A156676, A156774.

Programs

Magma

I:=[531, 1260]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

Mathematica

LinearRecurrence[{2,-1}, {531,1260}, 40]

PARI

a(n)=729*n-198 \\ Charles R Greathouse IV, Dec 23 2011

Sage

[9*(81*n -22) for n in [1..50]] # G. C. Greubel, Jun 19 2021

Formula

a(n) = 2*a(n-1) - a(n-2).

G.f.: x*(531 + 198*x)/(1-x)^2.

E.g.f.: 9*(22 - (22 - 81*x)*exp(x)). - G. C. Greubel, Jun 19 2021