A158770 a(n) = 1521*n^2 - 39.

1482, 6045, 13650, 24297, 37986, 54717, 74490, 97305, 123162, 152061, 184002, 218985, 257010, 298077, 342186, 389337, 439530, 492765, 549042, 608361, 670722, 736125, 804570, 876057, 950586, 1028157, 1108770, 1192425, 1279122, 1368861, 1461642, 1557465, 1656330

Offset

1,1

Comments

The identity (78*n^2-1)^2-(1521*n^2-39)*(2*n)^2 = 1 can be written as A158771(n)^2-a(n)*A005843(n)^2 = 1.

Links

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

Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]

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

Formula

G.f.: 39*x*(-38-41*x+x^2)/(x-1)^3.

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

From Amiram Eldar, Mar 23 2023: (Start)

Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(39))*Pi/sqrt(39))/78.

Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(39))*Pi/sqrt(39) - 1)/78. (End)

Maple

A158770:=n->1521*n^2-39: seq(A158770(n), n=1..50); # Wesley Ivan Hurt, May 03 2017

Mathematica

LinearRecurrence[{3, -3, 1}, {1482, 6045, 13650}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
Table[1521n^2-39, {n, 30}] (* Harvey P. Dale, Aug 23 2019 *)

Prog

(Magma) I:=[1482, 6045, 13650]; [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, Feb 21 2012
(PARI) for(n=1, 40, print1(1521*n^2 - 39", ")); \\ Vincenzo Librandi, Feb 21 2012

Crossrefs

Cf. A005843, A158771.

Sequence in context: A052167 A097024 A253331 * A252366 A253324 A204037

Adjacent sequences: A158767 A158768 A158769 * A158771 A158772 A158773

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 26 2009

Extensions

Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009

Status

approved