A157732 a(n) = 388962*n^2 - 430416*n + 119071.

77617, 814087, 2328481, 4620799, 7691041, 11539207, 16165297, 21569311, 27751249, 34711111, 42448897, 50964607, 60258241, 70329799, 81179281, 92806687, 105212017, 118395271, 132356449, 147095551, 162612577, 178907527

Offset

1,1

Comments

The identity (388962*n^2 - 430416*n + 119071)^2 - (441*n^2 - 488*n + 135)*(18522*n - 10248)^2 = 1 can be written as a(n)^2 - A157730(n)*A157731(n)^2 = 1.

This is the case s=21 and r=244 in the identity (2*(s^2*n-r)^2-1)^2 - (((s^2*n-r)^2-1)/s^2)*(2*s*(s^2*n-r))^2 = 1, where ((s^2*n-r)^2-1)/s^2 is an integer if r^2 == 1 (mod s^2). - Bruno Berselli, Apr 23 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: x*(77617 + 581236*x + 119071*x^2)/(1 - x)^3.

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

Mathematica

LinearRecurrence[{3, -3, 1}, {77617, 814087, 2328481}, 40]

Prog

(Magma) I:=[77617, 814087, 2328481]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 388962*n^2 - 430416*n + 119071.

Crossrefs

Cf. A157730, A157731.

Sequence in context: A206275 A249958 A232349 * A210123 A279893 A069044

Adjacent sequences: A157729 A157730 A157731 * A157733 A157734 A157735

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 05 2009

Status

approved