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 A270810 Expansion of (x - x^2 + 2*x^3 + 2*x^4)/(1 - 3*x + 2*x^2). 5

%I

%S 0,1,2,6,16,36,76,156,316,636,1276,2556,5116,10236,20476,40956,81916,

%T 163836,327676,655356,1310716,2621436,5242876,10485756,20971516,

%U 41943036,83886076,167772156,335544316,671088636,1342177276,2684354556,5368709116,10737418236,21474836476

%N Expansion of (x - x^2 + 2*x^3 + 2*x^4)/(1 - 3*x + 2*x^2).

%H Colin Barker, <a href="/A270810/b270810.txt">Table of n, a(n) for n = 0..1000</a>

%H M. Diepenbroek, M. Maus, A. Stoll, <a href="http://www.valpo.edu/mathematics-statistics/files/2014/09/Pudwell2015.pdf">Pattern Avoidance in Reverse Double Lists</a>, Preprint 2015. See Table 3.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F G.f.: x*(1 - x + 2*x^2 + 2*x^3)/((1 - x)*(1 - 2*x)).

%F a(n) = 5*2^(n-2)-4 for n>2. - _Bruno Berselli_, Apr 08 2016

%F a(n) = 3*a(n-1)-2*a(n-2) for n>4. - _Colin Barker_, Apr 12 2016

%F From _Paul Curtz_, Sep 23 2019: (Start)

%F a(n+1) = b(n+4) - b(n) where b(n) = 0, 1, 1, 1 followed by A026646.

%F a(n) = 2*a(n-1)+4 for n>4. (End)

%o (MAGMA) [n le 2 select n else 5*2^(n-2)-4: n in [0..40]]; // _Bruno Berselli_, Apr 08 2016

%o (PARI) concat(0, Vec(x*(1-x+2*x^2+2*x^3)/((1-x)*(1-2*x)) + O(x^50))) \\ _Colin Barker_, Apr 12 2016

%Y Agrees with A048487 except for initial terms.

%Y Cf. A002605, A265106, A265107, A265278.

%Y Cf. A026646, A000225.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Apr 06 2016

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Last modified October 18 07:42 EDT 2019. Contains 328146 sequences. (Running on oeis4.)