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%I #14 Oct 10 2021 22:59:31
%S 1,2,4,8,16,32,67,152,376,992,2704,7424,20233,54398,144112,376736,
%T 974368,2500544,6385435,16264220,41396788,105423776,268818064,
%U 686499008,1755723793,4495691834,11521647916,29543647160,75774096832,194353495424
%N a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 3^k * 2^(n-6k).
%C Binomial transform of 1,1,1,1,1,1,4,4,13,13,31,... with g.f. (1-x)^2(1+x)^3/(1-3x^2+3x^4-4x^6)=(1+x)(1-x^2)^2/((1-x^2)^3-3x^6).
%H Seiichi Manyama, <a href="/A100139/b100139.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,-12,8,0,0,3).
%F G.f.: (1-2x)^2/((1-2x)^3 - 3x^6).
%F a(n) = 6*a(n-1) -12*a(n-2) + 8*a(n-3) + 3*a(n-6).
%t LinearRecurrence[{6,-12,8,0,0,3},{1,2,4,8,16,32},30] (* _Harvey P. Dale_, Sep 30 2015 *)
%Y Cf. A097122, A100133, A100134, A100137, A100138.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 06 2004
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