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A261250 One half of the even entries of A033317. 7
1, 2, 1, 3, 1, 90, 2, 4, 2, 1, 6, 21, 5, 12, 910, 1, 2, 3, 6, 3, 2, 160, 1, 15, 12, 1794, 7, 45, 4550, 33, 6, 1, 10, 1287, 2, 113076990, 4, 8, 4, 2, 468, 15, 1, 133500, 215, 3315, 20, 3, 9, 3, 15498, 561, 26500, 1, 60, 630, 110532, 2, 3188676, 5, 10, 5, 2, 1557945, 65, 7570212227550, 1, 14, 6, 56648, 48, 455, 30, 14127 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

2*a(n) = y0(n) is the positive fundamental solution satisfying the Pell equation x0(n)^2 + D(n)*y0(n)^2 = +1 with D(n) coinciding apparently with Conway's rectangular numbers r(n) = A007969(n). The corresponding x0 values are given in A262024.

For a proof of this coincidence see the W. Lang link under A007969. - Wolfdieter Lang, Oct 04 2015

LINKS

Table of n, a(n) for n=1..74.

EXAMPLE

The [r(n), x0(n), y0(n)] values for n = 1..16 are:

[2, 3, 2], [5, 9, 4], [6, 5, 2], [10, 19, 6],

[12, 7, 2], [13, 649, 180], [14, 15, 4],

[17, 33, 8], [18, 17, 4], [20, 9, 2],

[21, 55, 12], [22, 197, 42], [26, 51, 10],

[28, 127, 24], [29, 9801, 1820], [30, 11, 2], ...

CROSSREFS

Cf. A033317, A033313, A000037, A007969, A262024, A262025.

Sequence in context: A218951 A096642 A263006 * A227860 A020779 A260721

Adjacent sequences:  A261247 A261248 A261249 * A261251 A261252 A261253

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Sep 16 2015

STATUS

approved

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Last modified February 20 10:25 EST 2018. Contains 299385 sequences. (Running on oeis4.)