A158403 841n^2 + 2n.

843, 3368, 7575, 13464, 21035, 30288, 41223, 53840, 68139, 84120, 101783, 121128, 142155, 164864, 189255, 215328, 243083, 272520, 303639, 336440, 370923, 407088, 444935, 484464, 525675, 568568, 613143, 659400, 707339, 756960, 808263, 861248

Offset

1,1

Comments

The identity (841*n+1)^2-(841*n^2+2*n)*29^2=1 can be written as A158404(n)^2-a(n)*29^2=1.

Links

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

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*(29^2*t+2)).

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

Formula

G.f.: x*(843+839*x)/(1-x)^3.

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

Mathematica

LinearRecurrence[{3, -3, 1}, {843, 3368, 7575}, 50]

Prog

(Magma) I:=[843, 3368, 7575]; [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) = 841*n^2 + 2*n.

Crossrefs

Cf. A158404.

Sequence in context: A004949 A252061 A031707 * A114359 A038013 A334183

Adjacent sequences: A158400 A158401 A158402 * A158404 A158405 A158406

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved