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A003674
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a(n) = 2^(n-1)*(2^n - (-1)^n).
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3
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0, 3, 6, 36, 120, 528, 2016, 8256, 32640, 131328, 523776, 2098176, 8386560, 33558528, 134209536, 536887296, 2147450880, 8590000128, 34359607296, 137439215616, 549755289600, 2199024304128, 8796090925056
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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REFERENCES
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M. Gardner, Riddles of the Sphinx, New Mathematical Library, M.A.A., 1987, p. 145. Math. Rev. 89i:00015.
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LINKS
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FORMULA
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G.f.: 3*x/((1+2*x)*(1-4*x)).
Given the 2 X 2 matrix M = [1,3; 3,1], a(n) = term (1,2) in M^n, n>0. - Gary W. Adamson, Aug 06 2010
a(n) = 2*a(n-1) + 8*a(n-2).
E.g.f.: (1/2)*(exp(4*x) - exp(-2*x)). (End)
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MATHEMATICA
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Table[(4^n-(-2)^n)/2, {n, 0, 40}] (* G. C. Greubel, Feb 17 2023 *)
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PROG
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(PARI) a(n)=if(n<0, 0, 2^(n-1)*(2^n-(-1)^n))
(Magma) [(4^n -(-2)^n)/2: n in [0..40]]; // G. C. Greubel, Feb 17 2023
(SageMath) [(4^n-(-2)^n)/2 for n in range(41)] # G. C. Greubel, Feb 17 2023
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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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