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%I #9 Aug 17 2017 12:56:12
%S 0,1,1,2,4,5,9,14,20,33,49,74,116,173,265,406,612,937,1425,2162,3300,
%T 5013,7625,11614,17652,26865,40881,62170,94612,143933,218953,333158,
%U 506820,771065,1173137,1784706,2715268,4130981,6284681,9561518,14546644,22130881,33669681
%N Expansion of x/((1-x)*(1-x^2-2*x^3)).
%C a(n+1) gives diagonal sums of Riordan array (1/(1-x),x(1+2x)) and partial sums of A052947. - _Paul Barry_, Jul 18 2005
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,-2).
%F a(n) = a(n-1)+a(n-2)+a(n-3)-2*a(n-4) - _Roger L. Bagula_, Mar 25 2005
%F a(n+1)=sum{k=0..n, sum{j=0..floor(k/2), C(j, k-2j)2^(k-2j)}}; - _Paul Barry_, Jul 18 2005
%t {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {-2, 1, 1, 1}}.{a[n - 4], a[n - 3], a[n - 2], a[n - 1]} a[0] = 0; a[1] = 1; a[2] = 1; a[3] = 2; a[n_Integer?Positive] := a[n] = a[n - 1] + a[n - 2] + a[n - 3] - 2a[n - 4]; aa = Table[a[n], {n, 0, 200}] - _Roger L. Bagula_, Mar 25 2005
%t CoefficientList[Series[x/((1-x)(1-x^2-2x^3)),{x,0,50}],x] (* or *) LinearRecurrence[{1,1,1,-2},{0,1,1,2},50] (* _Harvey P. Dale_, Aug 17 2017 *)
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Nov 17 2002
%E Edited by _N. J. A. Sloane_, Aug 29 2008 at the suggestion of R. J. Mathar
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