A157736 a(n) = 388962*n^2 - 347508*n + 77617.

119071, 938449, 2535751, 4910977, 8064127, 11995201, 16704199, 22191121, 28455967, 35498737, 43319431, 51918049, 61294591, 71449057, 82381447, 94091761, 106579999, 119846161, 133890247, 148712257, 164312191, 180690049

Offset

1,1

Comments

The identity (388962*n^2 - 347508*n + 77617)^2 - (441*n^2 - 394*n + 88)*(18522*n - 8274)^2 = 1 can be written as a(n)^2 - A157734(n)*A157735(n)^2 = 1.

This is the case s=21 and r=197 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*(119071 + 581236*x + 77617*x^2)/(1 - x)^3.

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

Mathematica

LinearRecurrence[{3, -3, 1}, {119071, 938449, 2535751}, 40]

Prog

(Magma) I:=[119071, 938449, 2535751]; [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 - 347508*n + 77617.

Crossrefs

Cf. A157734, A157735.

Sequence in context: A253867 A253874 A253540 * A031686 A262510 A262509

Adjacent sequences: A157733 A157734 A157735 * A157737 A157738 A157739

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 05 2009

Status

approved