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A158490 a(n) = 100*n^2 - 10. 2
90, 390, 890, 1590, 2490, 3590, 4890, 6390, 8090, 9990, 12090, 14390, 16890, 19590, 22490, 25590, 28890, 32390, 36090, 39990, 44090, 48390, 52890, 57590, 62490, 67590, 72890, 78390, 84090, 89990, 96090, 102390, 108890, 115590, 122490, 129590, 136890, 144390 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (20*n^2-1)^2 - (100*n^2-10)*(2*n)^2 = 1 can be written as A158491(n)^2 - a(n)*A005843(n)^2 = 1.
LINKS
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f: 10*x*(-9-12*x+x^2)/(x-1)^3.
From Amiram Eldar, Mar 05 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(10))*Pi/sqrt(10))/20.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(10))*Pi/sqrt(10) - 1)/20. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {90, 390, 890}, 20]
100*Range[40]^2-10 (* Harvey P. Dale, Apr 03 2019 *)
PROG
(Magma) I:=[90, 390, 890]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n)=100*n^2-10 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Sequence in context: A201103 A234991 A234984 * A304618 A187300 A237129
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 20 2009
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)