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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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Interleaving of A007283 and A000079 without initial terms 1 and 2.
Equals A029744 without first two terms. Agrees with A145751 for all terms listed there (up to 65536). Apparently equal to 3 followed by A090989.
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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Vincenzo Librandi, Table of n, a(n) for n = 1..2000
Index entries for linear recurrences with constant coefficients, signature (0,2).
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FORMULA
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a(n) = A027383(n-1) + 2.
a(n) = A052955(n) + 1 for n >=1.
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.
Sequence in context: A299252 A299253 A063759 * A145751 A277099 A146566
Adjacent sequences: A163975 A163976 A163977 * A163979 A163980 A163981
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus, Aug 07 2009
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STATUS
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approved
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