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A075836
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Numbers n such that 10*n^2 + 9 is a square.
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1
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0, 2, 4, 18, 80, 154, 684, 3038, 5848, 25974, 115364, 222070, 986328, 4380794, 8432812, 37454490, 166354808, 320224786, 1422284292, 6317101910, 12160109056, 54009348606, 239883517772, 461763919342, 2050932962736
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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
| J. J. O'Connor and E. F. Robertson, Pell's Equation
Eric Weisstein's World of Mathematics, Pell Equation.
Index to sequences with linear recurrences with constant coefficients, signature (0,0,38,0,0,-1).
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FORMULA
| Lim. n-> Inf. a(n)/a(n-3) = 19 + 6*Sqrt(10). Lim. n-> Inf. a(3*k)/a(3*k-1) = (11 + 2*Sqrt(10))/9. Lim. n-> Inf. a(3*k+1)/a(3*k) = (7 + 2*Sqrt(10))/3. Lim. n-> Inf. a(3*k+2)/a(3*k+1) = (7 + 2*Sqrt(10))/3. - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 16 2002
G.f. 2*x^2*(1+2*x+9*x^2+2*x^3+x^4) / ( 1-38*x^3+x^6 ). - R. J. Mathar, Jul 03 2011
a(n) = 2*A075873(n). - R. J. Mathar, Jul 03 2011
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CROSSREFS
| Sequence in context: A052689 A139104 A014448 * A120664 A095816 A020101
Adjacent sequences: A075833 A075834 A075835 * A075837 A075838 A075839
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KEYWORD
| nonn
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AUTHOR
| Gregory V. Richardson (omomom(AT)hotmail.com), Oct 14 2002
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