|
| |
|
|
A075841
|
|
2*n^2 - 9 is a square.
|
|
1
| |
|
|
3, 15, 87, 507, 2955, 17223, 100383, 585075, 3410067, 19875327, 115841895, 675176043, 3935214363, 22936110135, 133681446447, 779152568547, 4541233964835, 26468251220463, 154268273357943, 899141388927195
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Lim. n-> Inf. a(n)/a(n-1) = 3 + 2*Sqrt(2).
|
|
|
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) = 3*sqrt(2)/4*((1+sqrt(2))^(2*n-1)-(1-sqrt(2))^(2*n-1)) = 6*a(n-1) - a(n-2)
G.f.: 3x(1-x)/(1-6x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]
|
|
|
CROSSREFS
| Sequence in context: A191148 A001931 A180677 * A152596 A168503 A089022
Adjacent sequences: A075838 A075839 A075840 * A075842 A075843 A075844
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Gregory V. Richardson (omomom(AT)hotmail.com), Oct 14 2002
|
| |
|
|
