A158312 400n^2 + 2n.

402, 1604, 3606, 6408, 10010, 14412, 19614, 25616, 32418, 40020, 48422, 57624, 67626, 78428, 90030, 102432, 115634, 129636, 144438, 160040, 176442, 193644, 211646, 230448, 250050, 270452, 291654, 313656, 336458, 360060, 384462, 409664

Offset

1,1

Comments

The identity (400*n+1)^2-(400*n^2+2*n)*(20)^2=1 can be written as A158313(n)^2-a(n)*(20)^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*(20^2*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*(402+398*x)/(1-x)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {402, 1604, 3606}, 50]
Table[400n^2+2n, {n, 40}] (* Harvey P. Dale, Jun 11 2023 *)

Prog

(Magma) I:=[402, 1604, 3606]; [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) = 400*n^2 + 2*n.

Crossrefs

Cf. A158313.

Sequence in context: A031518 A104391 A250753 * A237177 A128767 A097740

Adjacent sequences: A158309 A158310 A158311 * A158313 A158314 A158315

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Status

approved