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A163978
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a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 4.
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3
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3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 131072, 196608, 262144, 393216, 524288, 786432, 1048576, 1572864, 2097152, 3145728
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OFFSET
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1,1
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COMMENTS
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Equals A029744 without first two terms. Agrees with A145751 for all terms listed there (up to 65536).
Binomial transform is A078057 without initial 1, second binomial transform is A048580, third binomial transform is A163606, fourth binomial transform is A163604, fifth binomial transform is A163605.
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LINKS
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FORMULA
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a(n) = (1/2)*(5 - (-1)^n)*2^((2*n - 1 + (-1)^n)/4).
G.f.: x*(3+4*x)/(1-2*x^2).
E.g.f.: (1/2)*(4*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x) - 4). - G. C. Greubel, Aug 24 2017
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MATHEMATICA
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Join[{3, 4}, LinearRecurrence[{0, 2}, {6, 8}, 50]] (* or *) Table[(1/2)*(5 - (-1)^n)*2^((2*n - 1 + (-1)^n)/4) , {n, 1, 50}] (* G. C. Greubel, Aug 24 2017 *)
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PROG
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(Magma) [ n le 2 select n+2 else 2*Self(n-2): n in [1..41] ];
(PARI) x='x+O('x^50); Vec(x*(3+4*x)/(1-2*x^2)) \\ G. C. Greubel, Aug 24 2017
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CROSSREFS
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Cf. A007283 (3*2^n), A000079 (powers of 2), A029744, A145751, A090989, A078057, A048580, A163606, A163604, A163605, A027383, A052955.
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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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