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A158764 a(n) = 38*(38*n^2-1). 2
1406, 5738, 12958, 23066, 36062, 51946, 70718, 92378, 116926, 144362, 174686, 207898, 243998, 282986, 324862, 369626, 417278, 467818, 521246, 577562, 636766, 698858, 763838, 831706, 902462, 976106, 1052638, 1132058, 1214366, 1299562, 1387646, 1478618, 1572478 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (76*n^2-1)^2 - (1444*n^2-38) * (2*n)^2 = 1 can be written as A158765(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.: 38*x*(-37-40*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(38))*Pi/sqrt(37))/76.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(37))*Pi/sqrt(38) - 1)/76. (End)
MATHEMATICA
Table[38 (38 n^2 - 1), {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1406, 5738, 12958}, 40] (* Harvey P. Dale, Jan 09 2012 *)
CoefficientList[Series[38 (- 37 - 40 x + x^2) / (x - 1)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 11 2013 *)
PROG
(Magma) [38*(38*n^2-1): n in [0..40]]; // Vincenzo Librandi, Sep 11 2013
(PARI) a(n)=38*(38*n^2-1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Sequence in context: A206680 A022058 A107522 * A035863 A045127 A210786
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 26 2009
EXTENSIONS
Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009
STATUS
approved

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Last modified May 28 18:29 EDT 2024. Contains 372919 sequences. (Running on oeis4.)