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A075839
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11*n^2 - 2 is a square.
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5
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1, 19, 379, 7561, 150841, 3009259, 60034339, 1197677521, 23893516081, 476672644099, 9509559365899, 189714514673881, 3784780734111721, 75505900167560539, 1506333222617099059, 30051158552174420641
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Lim. n -> inf. a(n)/a(n-1) = 10 + 3*sqrt(11).
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REFERENCES
| A. H. Beiler, "The Pellian", ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, New York, New York, pp. 248-268, 1966.
L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, p. 341-400.
Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics Source Series, V. 16); American Mathematical Society, Providence, Rhode Island, 1999, p. 139-147.
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LINKS
| Index entries for two-way infinite sequences
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
J. J. O'Connor and E. F. Robertson, Pell's Equation
Eric Weisstein's World of Mathematics, Pell Equation.
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FORMULA
| a(n) = ((3+sqrt(11))*(10+3*sqrt(11))^n - (3-sqrt(11))*(10-3*sqrt(11))^n)/(2*sqrt(11)). - Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 09 2002
G.f.: (1-x)/(1-20*x+x^2). a(n)=20*a(n-1)-a(n-2), n>1. - Michael Somos, Oct 29 2002
Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)) then a(n)=q(n, 18). - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 06 2002
G.f.: (1-x)/(1-20*x+x^2). a(n)=20*a(n-1)-a(n-2). a(-1-n)=a(n). - Michael Somos, Apr 18 2003
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PROG
| (PARI) a(n)=subst(poltchebi(n+1)+poltchebi(n), x, 10)/11
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CROSSREFS
| 11a(n)^2-9*A083043(n)^2=2.
Row 20 of array A094954.
Cf. A075844.
Sequence in context: A057685 A041686 A023283 * A158592 A072359 A094737
Adjacent sequences: A075836 A075837 A075838 * A075840 A075841 A075842
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KEYWORD
| easy,nonn
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AUTHOR
| Gregory V. Richardson (omomom(AT)hotmail.com), Oct 14 2002
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