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A114048
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x-values in the solution to x^2 - 19*y^2 = 1.
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2
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1, 170, 57799, 19651490, 6681448801, 2271672940850, 772362118440199, 262600848596726810, 89283516160768675201, 30356132893812752841530, 10320995900380175197444999, 3509108249996365754378458130
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This sequence is computed with g(1e9,19) in the pari program.
A pellian equation (Pell's equation) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2006
The corresponding values of y of this Pell equation are in A174765. - Vincenzo Librandi, Dec 21 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
Tanya Khovanova, Recursive Sequences
Author?, Title?
John Robertson, Home page.
Index to sequences with linear recurrences with constant coefficients, signature (340,-1).
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FORMULA
| a(1)=1, a(2)=170 then a(n)=340*a(n-1)-a(n-2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2006
G.f.: x*(1-170x)/(1-340x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
| (170^2-1)/19 = 39^2
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MATHEMATICA
| LinearRecurrence[{340, -1}, {1, 170}, 30] (* Vincenzo Librandi, Dec 21 2011 *)
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PROG
| (PARI) g(n, k) = for(y=0, n, x=k*y^2+1; if(issquare(x), print1(floor(sqrt(x))", ")))
(PARI) a(n)=real((170+39*quadgen(4*19))^n) /* Michael Somos Feb 15 2006 */
(PARI) a=vector(12); a[1]=1; a[2]=170; for(i=3, #a, a[i]=340*a[i-1]-a[i-2]); a (Cloitre)
(MAGMA) I:=[1, 170]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Dec 21 2011
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CROSSREFS
| Cf. A174765.
Sequence in context: A178499 A133328 A098244 * A187704 A185239 A015975
Adjacent sequences: A114045 A114046 A114047 * A114049 A114050 A114051
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KEYWORD
| nonn,easy
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Feb 01 2006
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2006
Offset changed from 0 to 1 and g.f. adapted by Vincenzo Librandi, Dec 21 2011
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