A157375 a(n) = 2401*n^2 - 980*n + 99.

1520, 7743, 18768, 34595, 55224, 80655, 110888, 145923, 185760, 230399, 279840, 334083, 393128, 456975, 525624, 599075, 677328, 760383, 848240, 940899, 1038360, 1140623, 1247688, 1359555, 1476224, 1597695, 1723968, 1855043, 1990920

Offset

1,1

Comments

The identity (2401*n^2-980*n+99)^2-(49*n^2-20*n +2)*(343*n-70)^2=1 can be written as a(n)^2-A157373(n)*A157374(n)^2=1. - Vincenzo Librandi, Jan 28 2012

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). - Vincenzo Librandi, Jan 28 2012

G.f.: x*(-1520-3183*x-99*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 28 2012

E.g.f.: (49*x*(49*x + 29) + 99)*exp(x) - 99. - G. C. Greubel, Feb 04 2018

Mathematica

LinearRecurrence[{3, -3, 1}, {1520, 7743, 18768}, 40] (* Vincenzo Librandi, Jan 28 2012 *)
Table[2401*n^2 - 980*n + 99, {n, 1, 30}] (* G. C. Greubel, Feb 04 2018 *)
CoefficientList[Series[(-1520-3183x-99x^2)/(-1+x)^3, {x, 0, 40}], x] (* Harvey P. Dale, Jul 27 2021 *)

Prog

(Magma) I:=[1520, 7743, 18768]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 28 2012
(PARI) for(n=1, 40, print1(2401*n^2 - 980*n + 99", ")); \\ Vincenzo Librandi, Jan 28 2012

Crossrefs

Cf. A157373, A157374.

Sequence in context: A356767 A112641 A203386 * A331659 A174746 A074906

Adjacent sequences: A157372 A157373 A157374 * A157376 A157377 A157378

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009

Status

approved