%I #24 Dec 24 2023 02:30:02

%S 1,1,1,1,1,1,3,9,21,41,71,113,173,269,443,777,1413,2577,4615,8065,

%T 13813,23413,39691,67801,116973,203337,354519,617345,1071197,1851677,

%U 3192731,5501033,9485621,16381185,28330119,49035777,84883621,146875717,253983307,438968761

%N a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^k.

%H Seiichi Manyama, <a href="/A100135/b100135.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 (3,-3,1,0,0,2).

%F G.f.: (1-x)^2/((1-x)^3 - 2*x^6).

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 2*a(n-6).

%t LinearRecurrence[{3,-3, 1, 0, 0, 2},{1,1,1,1,1,1},38] (* _James C. McMahon_, Dec 22 2023 *)

%Y Cf. A098575, A100134, A100136.

%K nonn,easy

%O 0,7

%A _Paul Barry_, Nov 06 2004