A157436 a(n) = 128*n^2 + 2528*n + 12481.

15137, 18049, 21217, 24641, 28321, 32257, 36449, 40897, 45601, 50561, 55777, 61249, 66977, 72961, 79201, 85697, 92449, 99457, 106721, 114241, 122017, 130049, 138337, 146881, 155681, 164737, 174049, 183617, 193441, 203521, 213857, 224449

Offset

1,1

Comments

The identity (128*n^2 + 2528*n + 12481)^2 - (4*n^2 + 79*n + 390)*(64*n + 632)^2 = 1 can be written as a(n)^2 - A157434(n)* A157435(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).

Formula

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

G.f.: x*(-12481*x^2 + 27362*x - 15137)/(x-1)^3. [corrected by Georg Fischer, May 11 2019]

Mathematica

LinearRecurrence[{3, -3, 1}, {15137, 18049, 21217}, 50]

Prog

(Magma) I:=[15137, 18049, 21217]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 128*n^2 + 2528*n + 12481.

Crossrefs

Cf. A157434, A157435.

Sequence in context: A004935 A004955 A004975 * A196495 A031623 A105924

Adjacent sequences: A157433 A157434 A157435 * A157437 A157438 A157439

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 01 2009

Extensions

Corrected by Charles R Greathouse IV, Jul 29 2010

Status

approved