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A113861
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(1/9)*((6n - 7)*2^(n-1) - (-1)^n).
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2
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0, 1, 5, 15, 41, 103, 249, 583, 1337, 3015, 6713, 14791, 32313, 70087, 151097, 324039, 691769, 1470919, 3116601, 6582727, 13864505, 29127111, 61050425, 127693255, 266571321, 555512263, 1155763769, 2401006023, 4980969017, 10319851975, 21355531833, 44142719431
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This sequence is connected with the Collatz problem (see the sequences A045883 and A001045). - Michel Lagneau, Jan 13 2012
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REFERENCES
| T. Etzion, On the stopping redundancy of Reed-Muller codes, IEEE Trans. Information Theory, submitted (2005); arXiv:cs.IT/0511056.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,0,-4).
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FORMULA
| a(n+1)-2*a(n) = A001045(n+2), Jacobsthal numbers. - Paul Curtz, Jul 05 2008
3a(n)-a(n+1)= -1, -2, 4*a(n). - Paul Curtz, Jul 05 2008
G.f.: x^2(1+2x)/((1+x)(1-2x)^2). a(n)+a(n+1)=A014480(n-1). [From R. J. Mathar, Nov 11 2008]
a(n) = 4*a(n-1)-4*a(n-2)+(-1)^(n+1), n>2. [From Gary Detlefs, Dec 19 2010]
a(n) = 3*a(n-1)-4*a(n-3), n>3. [From Gary Detlefs, Dec 19 2010]
a(n) = n*2^n - A045883(n). [Michel Lagneau, Jan 13 2012]
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MATHEMATICA
| Join[{0}, Numerator[CoefficientList[Series[(x+1)/((x-1)*(x^2+x-2)), {x, 0, 40}], x]]] (* From Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)
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PROG
| (PARI) a(n)=((6*n-7)<<(n-1)-(-1)^n)/9 \\ Charles R Greathouse IV, Jan 13 2012
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CROSSREFS
| Cf. A102301.
Sequence in context: A201157 A054888 A038066 * A080870 A102620 A053731
Adjacent sequences: A113858 A113859 A113860 * A113862 A113863 A113864
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 25 2006
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