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Expansion of 1/(1-2x-3x^3).
2

%I #6 Jun 13 2015 00:51:34

%S 1,2,4,11,28,68,169,422,1048,2603,6472,16088,39985,99386,247036,

%T 614027,1526212,3793532,9429145,23436926,58254448,144796331,359903440,

%U 894570224,2223529441,5526769202,13737249076,34145086475,84870480556

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

%C In general 1/(1-a*x-b*x^3) expands to sum{k=0..floor(n/3),C(n-2k,k)b^(n-2k)(a/b)^(n-3k)}.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,3).

%F a(n)=2a(n-1)+3a(n-3); a(n)=sum{k=0..floor(n/3), binomial(n-2k, k)3^(n-2k)(2/3)^(n-3k)}.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 20 2004