A156636 a(n) = 4394*n + 1820.

1820, 6214, 10608, 15002, 19396, 23790, 28184, 32578, 36972, 41366, 45760, 50154, 54548, 58942, 63336, 67730, 72124, 76518, 80912, 85306, 89700, 94094, 98488, 102882, 107276, 111670, 116064, 120458, 124852, 129246, 133640, 138034, 142428, 146822, 151216, 155610

Offset: 0

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 A156735(n)^2 - A156640(n)*a(n)^2 = 1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A156640, A156718, A156735.

Programs

Magma

I:=[1820, 6214]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

Mathematica

LinearRecurrence[{2,-1},{1820,6214},50]

PARI

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

Formula

G.f.: 26*(70+99*x)/(x-1)^2. - R. J. Mathar, Jan 05 2011

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

E.g.f.: 26*exp(x)*(70 + 169*x). - Elmo R. Oliveira, Dec 08 2024

Extensions

Offset corrected by R. J. Mathar, Jan 05 2011