A157364 a(n) = 4802*n^2 - 196*n + 1.

4607, 18817, 42631, 76049, 119071, 171697, 233927, 305761, 387199, 478241, 578887, 689137, 808991, 938449, 1077511, 1226177, 1384447, 1552321, 1729799, 1916881, 2113567, 2319857, 2535751, 2761249, 2996351, 3241057, 3495367

Offset: 1

Author

Vincenzo Librandi, Feb 28 2009

Keywords

• nonn
• easy

Comments

The identity (4802*n^2-196*n+1)^2-(49*n^2-2*n)*(686*n-14)^2=1 can be written as a(n)^2-A157362(n)*A157363(n)^2=1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Vincenzo Librandi, X^2-AY^2=1
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A157362, A157363.

Programs

Magma

I:=[4607, 18817, 42631]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

Mathematica

LinearRecurrence[{3,-3,1},{4607,18817,42631},50]
Table[4802n^2-196n+1,{n,30}] (* Harvey P. Dale, Jul 29 2021 *)

PARI

a(n) = 4802*n^2-196*n+1

Formula

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

G.f.: x*(x^2 + 4996*x + 4607)/(1-x)^3.

E.g.f.: (1 + 4606*x + 4802*x^2)*exp(x) - 1. - G. C. Greubel, Feb 02 2018