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A158770
a(n) = 1521*n^2 - 39.
2
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, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
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
Sequence in context: A052167 A097024 A253331 * A252366 A253324 A204037
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 26 2009
EXTENSIONS
Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009
STATUS
approved