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A106329
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Numbers k such that k^2 = 8*j^2 + 9.
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4
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3, 9, 51, 297, 1731, 10089, 58803, 342729, 1997571, 11642697, 67858611, 395508969, 2305195203, 13435662249, 78308778291, 456417007497, 2660193266691, 15504742592649, 90368262289203, 526704831142569, 3069860724566211, 17892459516254697, 104284896372961971
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OFFSET
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1,1
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COMMENTS
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The ratio a(n)/(2*j(n)) tends to sqrt(2) as n increases.
For n > 0, a(n+1) is the n-th almost Lucas-balancing number of first type (see Tekcan and Erdem). - Stefano Spezia, Nov 25 2022
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LINKS
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FORMULA
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a(1)=3, a(2)=9 then a(n) = 6*a(n-1)-a(n-2).
a(n) = 3*((3-2*sqrt(2))^(n-1) + (3+2*sqrt(2))^(n-1))/2. - Colin Barker, Oct 13 2015
E.g.f.: 3*exp(3*x)*(3*cosh(2*sqrt(2)*x) - 2*sqrt(2)*sinh(2*sqrt(2)*x)) - 9. - Stefano Spezia, Nov 25 2022
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MATHEMATICA
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CoefficientList[Series[3 x (1 - 3 x)/(1 - 6 x + x^2), {x, 0, 23}], x] (* Michael De Vlieger, Nov 02 2020 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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