A158132 144n^2 + 2n.

146, 580, 1302, 2312, 3610, 5196, 7070, 9232, 11682, 14420, 17446, 20760, 24362, 28252, 32430, 36896, 41650, 46692, 52022, 57640, 63546, 69740, 76222, 82992, 90050, 97396, 105030, 112952, 121162, 129660, 138446, 147520, 156882, 166532

Offset

1,1

Comments

The identity (144*n+1)^2-(144*n^2+2*n)*(12)^2=1 can be written as A158133(n)^2-a(n)*(12)^2=1.

Links

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

Vincenzo Librandi, X^2-AY^2=1

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(12^2*t+2))

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*(-142*x-146)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {146, 580, 1302}, 50]

Prog

(Magma) I:=[146, 580, 1302]; [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) = 144*n^2 + 2*n.

Crossrefs

Cf. A158133.

Sequence in context: A238028 A179572 A211838 * A043431 A183662 A183654

Adjacent sequences: A158129 A158130 A158131 * A158133 A158134 A158135

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 13 2009

Status

approved