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A106329 Numbers k such that k^2 = 8*(j^2) + 9. 1
3, 9, 51, 297, 1731, 10089, 58803, 342729, 1997571, 11642697, 67858611, 395508969, 2305195203, 13435662249, 78308778291, 456417007497, 2660193266691, 15504742592649, 90368262289203, 526704831142569, 3069860724566211, 17892459516254697, 104284896372961971 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The ratio k(n)/(2*j(n)) tends to sqrt(2) as n increases.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (6,-1).

FORMULA

k(1)=3, k(2)=9 then k(n) = 6*k(n-1)-k(n-2).

G.f.: 3*x(1-3*x)/(1-6*x+x^2). - Philippe Deléham, Nov 17 2008

a(n) = (3/2)*A003499(n-1).

a(n) = (3*((3-2*sqrt(2))^(n-1)+(3+2*sqrt(2))^(n-1)))/2. - Colin Barker, Oct 13 2015

PROG

(PARI) Vec((3-9*x)/(1-6*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Dec 28 2011

CROSSREFS

Cf. A103328.

Sequence in context: A058110 A261542 A171951 * A193521 A018966 A018996

Adjacent sequences:  A106326 A106327 A106328 * A106330 A106331 A106332

KEYWORD

nonn,easy

AUTHOR

Pierre CAMI, Apr 29 2005

STATUS

approved

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Last modified May 25 16:08 EDT 2017. Contains 287039 sequences.