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%I #35 Jun 16 2022 17:11:30
%S 0,1,5,15,41,103,249,583,1337,3015,6713,14791,32313,70087,151097,
%T 324039,691769,1470919,3116601,6582727,13864505,29127111,61050425,
%U 127693255,266571321,555512263,1155763769,2401006023,4980969017,10319851975,21355531833,44142719431
%N a(n) = (1/9)*((6*n - 7)*2^(n-1) - (-1)^n).
%C This sequence is connected with the Collatz problem (see the sequences A045883 and A001045). - _Michel Lagneau_, Jan 13 2012
%H G. C. Greubel, <a href="/A113861/b113861.txt">Table of n, a(n) for n = 1..1000</a>
%H T. Etzion, <a href="http://arxiv.org/abs/cs.IT/0511056">On the stopping redundancy of Reed-Muller codes</a>, IEEE Trans. Information Theory 52 (11) (2006) <a href="http://dx.doi.org/10.1109/TIT.2006.883542">4867-4879</a>; arXiv:cs.IT/0511056.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-4).
%F a(n+1) - 2*a(n) = A001045(n+2), Jacobsthal numbers. - _Paul Curtz_, Jul 05 2008
%F 3*a(n) - a(n+1) = -1, -2, 4*a(n). - _Paul Curtz_, Jul 05 2008
%F From _R. J. Mathar_, Nov 11 2008: (Start)
%F G.f.: x^2*(1+2*x)/((1+x)*(1-2*x)^2).
%F a(n) + a(n+1) = A014480(n-1). (End)
%F a(n) = 4*a(n-1) - 4*a(n-2) + (-1)^(n+1), n>2. - _Gary Detlefs_, Dec 19 2010
%F a(n) = 3*a(n-1) - 4*a(n-3), n>3. - _Gary Detlefs_, Dec 19 2010
%F a(n) = n*2^n - A045883(n). - _Michel Lagneau_, Jan 13 2012
%F Starting with "1" = triangle A059260 * A016813 as a vector, where A016813 = (4n + 1): [ 1, 5, 9, 13, ...]. - _Gary W. Adamson_, Mar 06 2012
%t Join[{0},Numerator[CoefficientList[Series[(x+1)/((x-1)*(x^2+x-2)),{x,0,40}],x]]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2012 *)
%t LinearRecurrence[{3,0,-4},{0,1,5},40] (* _Harvey P. Dale_, Jun 16 2022 *)
%o (PARI) a(n)=((6*n-7)<<(n-1)-(-1)^n)/9 \\ _Charles R Greathouse IV_, Jan 13 2012
%Y Cf. A102301.
%Y Cf. A059260, A016813.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, Jan 25 2006
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