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A075844 11*n^2 + 4 is a square. 1
0, 6, 120, 2394, 47760, 952806, 19008360, 379214394, 7565279520, 150926376006, 3010962240600, 60068318435994, 1198355406479280, 23907039811149606, 476942440816512840, 9514941776519107194, 189821893089565631040 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

COMMENTS

Lim. n-> Inf. a(n)/a(n-1) = 10 + 3*Sqrt(11).

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.

LINKS

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.

FORMULA

a(n) = ((10+3*Sqrt(11))^n - (10-3*Sqrt(11))^n) / Sqrt(11).

a(n) = 20*a(n-1) - a(n-2).

G.f.: 6*x / (1 - 20*x + x^2).

a(n) = 6*A075843(n). - R. J. Mathar, Jul 03 2011

a(n) = (1/3)*(A075839(n+1)-A075839(n)).

CROSSREFS

Sequence in context: A026337 A065888 A185757 * A029697 A196688 A126448

Adjacent sequences:  A075841 A075842 A075843 * A075845 A075846 A075847

KEYWORD

nonn

AUTHOR

Gregory V. Richardson (omomom(AT)hotmail.com), Oct 14 2002

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Last modified February 16 08:00 EST 2012. Contains 205881 sequences.