A157111 a(n) = 137842*n - 106846.

30996, 168838, 306680, 444522, 582364, 720206, 858048, 995890, 1133732, 1271574, 1409416, 1547258, 1685100, 1822942, 1960784, 2098626, 2236468, 2374310, 2512152, 2649994, 2787836, 2925678, 3063520, 3201362, 3339204, 3477046

Offset: 1

Author

Vincenzo Librandi, Feb 23 2009

Keywords

• nonn
• easy

Comments

The identity (5651522*n^2 - 8761372*n + 3395619)^2 - (1681*n^2 - 2606*n + 1010)*(137842*n - 106846)^2 = 1 can be written as A157112(n)^2 - A157110(n)*a(n)^2 = 1. - Vincenzo Librandi, Jan 25 2012

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. A157110, A157112.

Programs

Magma

I:=[30996, 168838]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 25 2012

Mathematica

LinearRecurrence[{2,-1},{30996,168838},40] (* Vincenzo Librandi, Jan 25 2012 *)
Table[137842 n-106846,{n,30}] (* Harvey P. Dale, Dec 02 2024 *)

PARI

a(n)=137842*n-106846 \\ Charles R Greathouse IV, Dec 28 2011

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 25 2012

G.f.: x*(106846*x + 30996)/(x-1)^2. - Vincenzo Librandi, Jan 25 2012