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Search: id:A007179
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| A007179 |
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Dual pairs of integrals arising from reflection coefficients.
(Formerly M3284)
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+0
6
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| 0, 1, 1, 4, 6, 16, 28, 64, 120, 256, 496, 1024, 2016, 4096, 8128, 16384, 32640, 65536, 130816, 262144, 523776, 1048576, 2096128, 4194304, 8386560, 16777216, 33550336, 67108864, 134209536, 268435456
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Heading, Theorem relating to the development of a reflection coefficient in terms of a small parameter, J. Phys. A 14 (1981), 357-367.
Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
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FORMULA
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Binomial transform is (A000244(n)+A001333(n))/2. G.f. : x(1+x)/((1+2x)(1-2x^2)); a(n)=2a(n-1)+2a(n-2)-4a(n-3); a(n)=2^n/2-2^(n/2)(1+(-1)^n)/4. - Paul Barry (pbarry(AT)wit.ie), Apr 28 2004
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MAPLE
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f := n-> if n mod 2 = 0 then 2^(n-1)-2^((n-2)/2) else 2^(n-1); fi;
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CROSSREFS
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Sequence in context: A122537 A059736 A102731 this_sequence A112576 A081487 A099430
Adjacent sequences: A007176 A007177 A007178 this_sequence A007180 A007181 A007182
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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