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%I #13 Oct 10 2021 22:59:18
%S 1,2,4,8,16,32,65,136,296,672,1584,3840,9473,23566,58736,146080,
%T 361760,891328,2184961,5331476,12958684,31400160,75910320,183220800,
%U 441787201,1064687642,2565404524,6181873208,14899796416,35922756992,86635757825
%N a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^(n-6k).
%C Binomial transform of 1,1,1,1,1,1,2,2,2,5,5,11,11,... with g.f. (1-x)^2(1+x)^2/(1-3x^2+3x^4-2x^6)=(1+x)(1-x^2)^2/((1-x^2)^3-x^6).
%H Seiichi Manyama, <a href="/A100137/b100137.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8,0,0,1).
%F G.f.: (1-2x)^2/((1-2x)^3 - x^6).
%F a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) + a(n-6).
%t Table[Sum[Binomial[n-3k,3k]2^(n-6k),{k,0,Floor[n/6]}],{n,0,30}] (* or *) LinearRecurrence[{6,-12,8,0,0,1},{1,2,4,8,16,32},31] (* _Harvey P. Dale_, Mar 19 2015 *)
%Y Cf. A024493, A100131, A100134, A100137, A100138.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 06 2004
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