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A275794 One half of the y members of the positive proper solutions (x = x1(n), y = y1(n)) of the first class for the Pell equation x^2 - 2*y^2 = +7^2. 6
2, 15, 88, 513, 2990, 17427, 101572, 592005, 3450458, 20110743, 117214000, 683173257, 3981825542, 23207779995, 135264854428, 788381346573, 4595023225010, 26781758003487, 156095524795912, 909791390771985, 5302652819835998, 30906125528244003 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
See A275793(n) for the x1(n) members and details as well as a reference.
LINKS
FORMULA
a(n) = 15*S(n-1,6) - 2*S(n-2,6), with the Chebyshev polynomials S(n, 6) = A001109(n+1) for n >= -1, with S(-2, 6) = -1.
O.g.f: (2 + 3*x)/(1 - 6*x + x^2).
a(n) = 6*a(n-1) - a(n-2) for n >= 1, with a(-1) = -3 and a(0) = 2.
a(n) = (((3-2*sqrt(2))^n*(-9+4*sqrt(2))+(3+2*sqrt(2))^n*(9+4*sqrt(2)))) / (4*sqrt(2)). - Colin Barker, Sep 28 2016
EXAMPLE
See A275793.
MATHEMATICA
CoefficientList[Series[(2 + 3*x)/(1 - 6*x + x^2), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jan 29 2017 *)
LinearRecurrence[{6, -1}, {2, 15}, 30] (* Harvey P. Dale, May 30 2018 *)
PROG
(PARI) a(n) = round((((3-2*sqrt(2))^n*(-9+4*sqrt(2))+(3+2*sqrt(2))^n*(9+4*sqrt(2))))/(4*sqrt(2))) \\ Colin Barker, Sep 28 2016
(PARI) Vec((2+3*x)/(1-6*x+x^2) + O(x^30)) \\ Colin Barker, Oct 02 2016
CROSSREFS
Sequence in context: A153445 A208974 A294196 * A037746 A037627 A192369
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 27 2016
STATUS
approved

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Last modified July 15 23:38 EDT 2024. Contains 374343 sequences. (Running on oeis4.)