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A084169
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A Pell Jacobsthal product.
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1
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0, 1, 2, 15, 60, 319, 1470, 7267, 34680, 168435, 810898, 3921103, 18918900, 91381991, 441150502, 2130258075, 10285325040, 49663079099, 239791814010, 1157823924167, 5590452446700, 26993130847215, 130334271942158
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (2^n - (-1)^n)*( (1+sqrt(2))^n - (1-sqrt(2))^n )/(6*sqrt(2)).
G.f.: x*(1-2*x^2)/((1+2*x-x^2)*(1-4*x-4*x^2)). - Colin Barker, May 01 2012
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MATHEMATICA
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LinearRecurrence[{2, 13, 4, -4}, {0, 1, 2, 15}, 41] (* G. C. Greubel, Oct 11 2022 *)
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PROG
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(Magma) [0] cat [(2^n-(-1)^n)*Evaluate(DicksonSecond(n-1, -1), 2)/3: n in [1..40]]; // G. C. Greubel, Oct 11 2022
(SageMath)
def A084169(n): return (2^n-(-1)^n)*lucas_number1(n, 2, -1)/3
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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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