A156627 a(n) = 4394*n - 1820.

2574, 6968, 11362, 15756, 20150, 24544, 28938, 33332, 37726, 42120, 46514, 50908, 55302, 59696, 64090, 68484, 72878, 77272, 81666, 86060, 90454, 94848, 99242, 103636, 108030, 112424, 116818, 121212, 125606, 130000, 134394, 138788, 143182

Offset: 1

Author

Vincenzo Librandi, Feb 15 2009

Keywords

• nonn
• easy

Comments

The identity (57122*n^2 - 47320*n + 9801)^2 - (169*n^2 - 140*n + 29)*(4394*n - 1820)^2 = 1 can be written as A156721(n)^2 - A156639(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. A156639, A156718, A156721.

Programs

Magma

I:=[2574,6968]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

Mathematica

LinearRecurrence[{2, -1}, {2574, 6968}, 40]

PARI

a(n)=4394*n-1820 \\ Charles R Greathouse IV, Dec 23 2011

Formula

G.f.: x*(2574 + 1820*x)/(1 - x)^2.

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